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Questions and Answers
How many different groupings of three fruit juice flavors can be selected from a possible 10 flavors?
What is the probability of selecting a particular combination of three fruit juice flavors out of a possible 10 flavors?
What is the number of 3-digit numbers that can be formed from the 5-digit number 12345 if repetition is not allowed?
How many combinations of 4 are there, taken 2 at a time?
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In a club, there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there?
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A store has 6 TV Graphics Magazines and 8 News-times Magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.
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A box contains 24 transistors, 4 of which are defective. What is the probability of selecting a defective transistor?
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How many combinations of 5 are there, taken 3 at a time?
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What is the number of permutations of 5 items taken 3 at a time?
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A committee of 2 women and 3 men is to be chosen from a group of 8 women and 6 men. How many different possibilities are there?
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Study Notes
Complement of an Event
- The complement of an event E is the event of E not occurring, denoted by Ä’
- P(E) + P(Ä’) = 1 or P(E) = 1 - P(Ä’), similarly P(Ä’) = 1 - P(E)
Mutually Exclusive Events
- Two events are said to be mutually exclusive if they can never occur at the same time
- Examples: being a Muslim and a Christian, being male or female
- Selecting a ball from a container, not replacing it, and then selecting a second ball
Dependent Events
- If two events A and B are dependent, then the probability of event A and B occurring is given by P(A and B) = P(A) × P(B|A)
- P(B|A) denotes the probability that event B occurs given that event A has already occurred
- Conditional probability problems can also be given in a table form, called a contingency table
Conditional Probability
- Example: An examiner wants to select two candidates at random from a distribution of males and females
- Solution: Use conditional probability to find the probability of selecting the second candidate given the first candidate
- Example: A student has a 75% chance of passing paper 1 and a conditional 50% chance of passing paper 2 given that he passed paper 1
- Solution: Find the probability that the student passes paper 2 given that he passed paper 1
Fundamentals of Counting Rule
- Permutation: the number of different arrangements of objects
- Combination: the number of different groupings of objects without regard to order
- Example: In how many different ways can six new cars be displayed on a showroom floor? Solution: 6! = 720 ways
- Example: How many possible combinations of three equities can an investment portfolio consist of, if there is a choice of four Property equities, ten Financial equities, and six Mining equities?
More Examples
- Example: How many 3-digit numbers can be formed from the 5-digit number 12345 if repetition is not allowed and if repetition is allowed
- Example: In a club, how many different possibilities are there to choose a committee of 3 women and 2 men?
- Example: A store has 6 TV Graphics Magazines and 8 News-times Magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.
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Description
Test your understanding of probability theory with this quiz, covering concepts such as events, complements, mutually exclusive events, and conditional probability. Learn how to apply the rules of probability to solve problems.
