Questions and Answers
What is the probability that a fair, six-sided die rolls a 6?
1/6
If the probability that the president doesn't declare war is 0.98, then what is the probability that the president does declare war?
0.02
If the probability of a NASCAR racer making it through the race without a crash is 0.8 and the probability of a frog living to old age is 0.15, what is the probability that one of these events occurs?
0.95
In the same scenario, what is the probability that both events occur?
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What is the probability of either an engine failing on a plane or the plane crashing if the probability of an engine failure is 0.2, the probability of a plane crash is 0.1, and the probability of both is 0.02?
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If a school has 150 girl students and 256 athletes (of which 100 are girls), what is the probability that a student is a girl given that they are an athlete?
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Are being a Ford and having good tires independent events if the probability of a car being a Ford is 0.34 and the probability of a car being a Ford given that it has good tires is also 0.34?
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What is the probability of a fair coin landing heads on the tenth time it is flipped?
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If the probability of a dictator starting a genocide is 0.99, and the probability of the UN dismantling his dictatorship is 0.001, what is the probability of both events occurring?
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If the probability of getting turkey is 0.3 and the probability of getting ham is 0.4, what is the probability of getting turkey or ham if the probability of getting both is 0.12?
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Study Notes
Probability of Rolling a Die
- The probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.166667.
Probability of Declaration of War
- If the probability of the president not declaring war is 0.98, then the probability of him declaring war is 0.02 (1 - 0.98).
Disjoint Events in Racing and Frog Lifespan
- The probability of either a NASCAR racer avoiding a crash (0.8) or a frog living to old age (0.15) is calculated as 0.95 (0.8 + 0.15).
Independent Events in Racing Crashes
- For events of the racer avoiding a crash and the frog living to old age, the probability of both occurring is 0.12 (0.8 x 0.15).
Non-exclusive Events with Plane Failures
- The probability of experiencing either an engine failure (0.2) or a plane crash (0.1) is 0.28 when considering their joint occurrence (0.02) using the general addition rule.
Conditional Probability of Athletes
- In a school with 400 students (150 girls and 256 athletes), the probability that an athlete is a girl is approximately 39.05% (100/400 divided by 256/400).
Independence of Events With Cars
- The events of a car being a Ford and having good tires are independent since the probability remains the same whether or not the car has good tires (0.34).
Coin Flip Probability
- The probability of flipping heads on the tenth flip of a fair coin is 0.5; this remains constant regardless of the number of flips.
Genocide and Dismantling Probability
- The joint probability of a dictator starting a genocide (0.99) and the UN dismantling the dictatorship (0.001) is 0.00099 (0.99 x 0.001).
Probability of Dinner Choices
- The probability of getting either turkey (0.3) or ham (0.4), given a joint probability of both (0.12), is 0.58 (0.3 + 0.4 - 0.12).
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Description
This quiz offers practice problems on the fundamentals of probability, including calculating the probability of specific outcomes with dice and events. It helps reinforce key concepts and formulas used in probability theory.
