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What is the probability that all extracted pencils are of different colors from a box containing 5 red, 6 green, and 4 blue pencils?
What is the probability that all extracted pencils are of different colors from a box containing 5 red, 6 green, and 4 blue pencils?
What is the probability that refrigerators of one mark remain unsold if 12 out of 15 refrigerators have been sold, assuming all marks have an equal probability of being sold?
What is the probability that refrigerators of one mark remain unsold if 12 out of 15 refrigerators have been sold, assuming all marks have an equal probability of being sold?
If there are 20 balls in an urn, 3 red, 2 blue, and 15 white, what is the probability of selecting a red or blue ball?
If there are 20 balls in an urn, 3 red, 2 blue, and 15 white, what is the probability of selecting a red or blue ball?
What is the sum of the probabilities of events A1, A2,…, An that form a complete group?
What is the sum of the probabilities of events A1, A2,…, An that form a complete group?
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Given that the probability of a rainy day is p = 0.75, what is the probability that the day will be clear?
Given that the probability of a rainy day is p = 0.75, what is the probability that the day will be clear?
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What is the probability of hitting the target in either the second area or the third area if the hit probability in the first area is 0.5 and in the second area is 0.3?
What is the probability of hitting the target in either the second area or the third area if the hit probability in the first area is 0.5 and in the second area is 0.3?
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If two incompatible events are present, what is the sum of their probabilities?
If two incompatible events are present, what is the sum of their probabilities?
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What is the conditional probability of event A occurring given that event B has already happened?
What is the conditional probability of event A occurring given that event B has already happened?
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What is the probability of rolling a number that is greater than 3 and even when a die is rolled?
What is the probability of rolling a number that is greater than 3 and even when a die is rolled?
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If two events each have a probability of 0.3 and are independent, what is the probability that neither event occurs?
If two events each have a probability of 0.3 and are independent, what is the probability that neither event occurs?
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How many different 3-letter arrangements can be formed using the letters in the word ABSENT?
How many different 3-letter arrangements can be formed using the letters in the word ABSENT?
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What is the probability that a female selected randomly from a class of 460 females and 540 males failed if 13% of females failed?
What is the probability that a female selected randomly from a class of 460 females and 540 males failed if 13% of females failed?
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What is the total number of different 2-member teams that can be formed from six students?
What is the total number of different 2-member teams that can be formed from six students?
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How many possible license plates can be issued if the format is two letters followed by two numbers?
How many possible license plates can be issued if the format is two letters followed by two numbers?
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How is the value of 0! + 1! + 4! evaluated?
How is the value of 0! + 1! + 4! evaluated?
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If a fair coin is tossed five times, what is the probability that the fifth toss is heads, given that the first four were heads?
If a fair coin is tossed five times, what is the probability that the fifth toss is heads, given that the first four were heads?
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What is the probability that the second taken cylinder is elliptic given that the first was conic?
What is the probability that the second taken cylinder is elliptic given that the first was conic?
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What is the probability of drawing a white ball first, then a black ball, followed by a blue ball from an urn containing 4 white, 5 black, and 6 blue balls?
What is the probability of drawing a white ball first, then a black ball, followed by a blue ball from an urn containing 4 white, 5 black, and 6 blue balls?
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Given P(A) = 0.1, P(B) = 0.49, and P(C) = 0.3, what is the probability of event D?
Given P(A) = 0.1, P(B) = 0.49, and P(C) = 0.3, what is the probability of event D?
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If the probability of hitting the target with the first gun is 0.3 and with the second gun is 0.5, what is the probability of hitting the target with both guns?
If the probability of hitting the target with the first gun is 0.3 and with the second gun is 0.5, what is the probability of hitting the target with both guns?
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What is the probability that all three selected details from three boxes will be standard, if the first box has 5 standard details, the second has 6, and the third has 3?
What is the probability that all three selected details from three boxes will be standard, if the first box has 5 standard details, the second has 6, and the third has 3?
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What is the probability of at least two hits when shooting at a target with three guns that have hit probabilities of p1 = 0.6, p2 = 0.7, and p3 = 0.5?
What is the probability of at least two hits when shooting at a target with three guns that have hit probabilities of p1 = 0.6, p2 = 0.7, and p3 = 0.5?
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What is the probability that at least one of the three flat-printing machines at a typography works, if each has a working probability of 0.6?
What is the probability that at least one of the three flat-printing machines at a typography works, if each has a working probability of 0.6?
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What is the probability that exactly two hits occur in three shots at a target where each shot has a probability of hit equal to 0.6?
What is the probability that exactly two hits occur in three shots at a target where each shot has a probability of hit equal to 0.6?
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How many two-place numbers can be made of the digits 1, 4, 5, and 7 if each digit is included only once?
How many two-place numbers can be made of the digits 1, 4, 5, and 7 if each digit is included only once?
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How many ways are there to choose 2 details from a box containing 9 details?
How many ways are there to choose 2 details from a box containing 9 details?
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If object A can be chosen by m ways and object B can be chosen by n ways, how many ways can either A or B be chosen?
If object A can be chosen by m ways and object B can be chosen by n ways, how many ways can either A or B be chosen?
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What defines events as equally possible?
What defines events as equally possible?
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What is the probability of a reliable event?
What is the probability of a reliable event?
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What is the probability of an impossible event?
What is the probability of an impossible event?
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What range does the probability of a random event fall into?
What range does the probability of a random event fall into?
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How is the relative frequency of an event A defined?
How is the relative frequency of an event A defined?
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What is the probability that a randomly selected male student did not pass?
What is the probability that a randomly selected male student did not pass?
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What is the probability that a student who can solve 6 out of 10 problems will solve exactly five problems when 8 questions are selected randomly?
What is the probability that a student who can solve 6 out of 10 problems will solve exactly five problems when 8 questions are selected randomly?
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If 10% of people are left-handed, what is the probability that exactly 2 out of 6 randomly selected people are left-handed?
If 10% of people are left-handed, what is the probability that exactly 2 out of 6 randomly selected people are left-handed?
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What is the probability that not all of 4 tested computer chips fail if 15% are rejected?
What is the probability that not all of 4 tested computer chips fail if 15% are rejected?
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Which statement correctly defines the union of two events A and B?
Which statement correctly defines the union of two events A and B?
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What is the probability that a randomly chosen student from a class of 20 students under the age of 10 is also under 11?
What is the probability that a randomly chosen student from a class of 20 students under the age of 10 is also under 11?
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In a CD with 12 songs where the first five are rock and the rest are ballads, what is the probability of first listening to a ballad?
In a CD with 12 songs where the first five are rock and the rest are ballads, what is the probability of first listening to a ballad?
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If two fair dice are rolled and the total is 6, what is the probability that the red die shows a 3?
If two fair dice are rolled and the total is 6, what is the probability that the red die shows a 3?
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What is the probability that the problem given to three students with chances 2/3, 3/4, and 2/5 will be solved?
What is the probability that the problem given to three students with chances 2/3, 3/4, and 2/5 will be solved?
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What is the probability that at least one of a boy or a girl passes an M.B.A. examination if the boy has a 1/5 chance of failing and the girl has a 3/5 chance?
What is the probability that at least one of a boy or a girl passes an M.B.A. examination if the boy has a 1/5 chance of failing and the girl has a 3/5 chance?
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If an urn contains 10 balls and the probability that both drawn balls are the same color is 0.54, how many blue balls are in the second urn?
If an urn contains 10 balls and the probability that both drawn balls are the same color is 0.54, how many blue balls are in the second urn?
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In a bag with 6 red discs and 4 blue discs, what is the conditional probability that all three drawn discs will be blue given that at least one is blue?
In a bag with 6 red discs and 4 blue discs, what is the conditional probability that all three drawn discs will be blue given that at least one is blue?
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If a bag contains 4 white, 6 red, and 10 black balls, what is the formula to calculate the probability that at least one ball drawn with replacement is white?
If a bag contains 4 white, 6 red, and 10 black balls, what is the formula to calculate the probability that at least one ball drawn with replacement is white?
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Given two sets of details where the probability of a standard detail from the first set is 0.7 and from the second set is 0.4, what is the probability that a randomly chosen detail is not standard?
Given two sets of details where the probability of a standard detail from the first set is 0.7 and from the second set is 0.4, what is the probability that a randomly chosen detail is not standard?
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Which expression indicates the occurrence of exactly one of the events A, B, C?
Which expression indicates the occurrence of exactly one of the events A, B, C?
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What is the probability that exactly one of the boy or girl passes the examination, given their failure probabilities of 1/5 and 3/5 respectively?
What is the probability that exactly one of the boy or girl passes the examination, given their failure probabilities of 1/5 and 3/5 respectively?
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Study Notes
Permutations, Combinations, Allocations
- Permutation formula: Pn = n! or Pn-m =(n!)/(m!*(n-m)!)
- Allocation formula: Anm = n!/(n − m)!
- Combination formula: nCm = n! / (m! * (n − m)!)
Two-Place Numbers
- Using digits {1, 4, 5, 7}, there are 24 two-place numbers possible without repetition.
- There are 12 two-place numbers possible if repetition is allowed (using digits 1, 4, 5, 7)
Ways to Choose Details
- From a box of 9 details, choosing 2 can be done in 36 ways.
Relationships Between Allocations, Permutations, and Combinations
- Am = PmCm
- The formulas for allocations, permutations, and combinations are related.
Equally Possible Events
- Events are equally possible if there is no reason to believe one event is more likely than another.
Probability of an Event
- Probability formula: P(A) = (favorable outcomes)/(total possible outcomes)
- Probability of a certain event = 1
- Probability of an impossible event = 0
Relative Frequency
- Relative frequency of event A = number of times A occurred / total number of trials
Probability of a Random Event
- The probability of a random event is a positive number between 0 and 1.
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Description
This quiz focuses on the fundamental principles of permutations, combinations, and allocations, along with their relationships. You'll also explore concepts of equally possible events and the probability of an event, using relevant formulas to solve problems. Test your understanding of these core mathematical ideas in combinatorics and probability.
