Randomness, Probability, and Simulation

You roll a standard number cube once. What is the probability of rolling a number less than 4?

Answer explanation

The probability of rolling a number less than 4 is 3/6, which simplifies to 1/2. This is because there are 3 numbers (1, 2, and 3) that are less than 4 out of the 6 possible outcomes.

You roll a standard number cube once. What is the probability of rolling a number divisible by 3?

Answer explanation

The probability of rolling a number divisible by 3 is 2/6, which simplifies to 1/3. This is the correct choice because it represents the probability of rolling a number that is a multiple of 3.

Suppose a married man and woman both carry a gene for cystic fibrosis but don't have the disease themselves. According to the laws of genetics, the probability that any child they have will develop cystic fibrosis is 0.25. Explain what this probability means. (Remember to change it to a percent!)

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According to The Book of Odds, the probability that a randomly selected US adult drinks coffee on a given day is 0.56. Explain what this probability means. (Remember to change it to a percent!)

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Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red. Explain what this probability means.

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A college basketball player makes about 75% of her free throws. In one game, the player makes her first 5 free-throw attempts. When the player steps to the free-throw line for her sixth attempt, a radio announcer says that she is "due for a miss". Explain why the announcer is wrong.

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Imagine tossing a coin 6 times and recording heads (H) or tails (T) on each toss. Which of the following outcomes is more likely?

• HTHTTH

• TTTHHH

• Equally Likely

Imagine rolling a die 12 times and recording the result of each roll. Which of the following outcomes is more likely?

• 1 2 3 4 5 6 6 5 4 3 2 1

• 1 5 4 5 2 4 3 3 6 1 2 6

• Equally Likely

A randomly selected US adult male has probability about 0.07 (7%) of having some form of red-green color blindness. Suppose we choose 4 US adult males at random. What's the probability that at least one of them is red-green color-blind?

• High

• 50/50

• Low

Suppose that 4 friends get together to study at Leigh's house for their next statistics test. When they go for a snack in the kitchen, Leigh's 3-year-old brother makes a tower using their textbooks. Unfortunately, none of the students has written his or her name in the books, so when they leave, each student takes one of the books at random. When the students return the books at the end of the year and the clerk scans their barcodes, the students are surprised to learn that none of the 4 had their own book. What's the probability that none of the 4 students ended up with the correct book?

• High

• 50/50

• Low