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Questions and Answers
Which of the following can never be a probability of an outcome?
When two coins are tossed, what is the probability of getting 1 head and 1 tail?
What is the probability of rolling a number greater than 2 with a single die?
If P(A) = 0.48 and P(B) = 0.81, what is P(A or B)?
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What is the probability that the sum of two rolled dice is at least 11?
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Which of the following values can be a probability? (Select all that apply)
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The probability of rolling a die and getting a 6 is the same as the probability of rolling a die and getting a 5.
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What is the sample space when two coins are tossed?
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The probability that a randomly selected high school student does not play organized sports is ___
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Match the following probabilities with their associated events:
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Study Notes
Probability Basics
- Probability of an event must be between 0 and 1, inclusive.
- Probability cannot be negative or greater than 1.
- 5/4, -0.25, and 1.03 are not valid probabilities.
Coin Tosses
- Sample space for tossing two coins: {HH, HT, TH, TT}
- Probability of both heads (HH): 1/4
- Probability of one head and one tail (HT or TH): 2/4 = 1/2
Rolling Dice
- Probability of rolling a 5 or 6: 2/6 = 1/3
- Probability of rolling a number greater than 2: 4/6 = 2/3
- Probability of rolling a sum of 6 with two dice: 5/36
- Possible combinations: (1,5), (2,4), (3,3), (4,2), (5,1)
- Probability of rolling a sum of at least 11 with two dice: 3/36 = 1/12
- Possible combinations: (5,6), (6,5), (6,6)
High School Sports Survey
- Probability of a randomly selected student playing sports: 288/500 = 0.576
- Probability of a randomly selected student not playing sports: 212/500 = 0.424
Conditional Probability
- P(Ac) (probability of the complement of A) = 1 - P(A) = 1 -0.48 = 0.52.
- P(A or B) = P(A) + P(B) - P(A and B) = 0.48 + 0.81 - 0.32 = 0.97
- P(B|A) (probability of B given A) = P(A and B) / P(A) = 0.32 / 0.48 = 2/3
Probability
- Probabilities can range from 0 to 1, inclusive.
- A probability greater than 1 or less than 0 is invalid.
- 5/4, -0.25, and 1.03 are invalid probabilities.
Coin Toss Sample Space
- The possible events for tossing two coins are: HH, HT, TH, TT.
- The probability of getting two heads (HH) is 1/4.
- The probability of getting one head and one tail (HT or TH) is 2/4 or 1/2.
Die Roll Probabilities
- The probability of rolling a 5 or a 6 on a single die is 2/6 or 1/3.
- The probability of rolling a number greater than 2 is 4/6 or 2/3.
- The probability of rolling a sum of 6 with two dice is 5/36.
- The probability of rolling a sum of at least 11 with two dice is 3/36 or 1/12.
Sports Participation Probabilities
- The probability of a randomly selected student playing organized sports is 288/500 or 0.576.
- The probability of a randomly selected student not playing organized sports is 212/500 or 0.424.
Conditional Probability
- The probability of the complement of A (Ac) is 1 - P(A) = 1 - 0.48 = 0.52.
- The probability of A or B is P(A) + P(B) - P(A and B) = 0.48 + 0.81 - 0.32 = 0.97.
- The conditional probability of B given A (B|A) is P(A and B) / P(A) = 0.32 / 0.48 = 2/3.
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Description
Explore the fundamentals of probability through various scenarios including coin tosses, rolling dice, and sports surveys. This quiz will test your understanding of valid probabilities and conditional probability concepts. Perfect for high school students studying basic probability principles.
