Conditional Probability

If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this?

• If you flip three coins 1000 times, you will get three heads exactly 125 times.

• If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125.

• If you have 20 sets of three coin flips, then at least one set of flips will be three heads.

• If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.

• If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.

Forrest has determined that if he gets to the bus stop at 7:30 am, there is a 0.15 probability that he misses the bus. If he arrives at the bus stop three consecutive days at 7:30, what is the approximate probability that he catches the bus all three days?

• 0.003

• 0.386

• 0.450

• 0.614

• 0.997

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 Americans are randomly selected, what is the probability that at least 1 of them is a universal donor?

• 0

• 0.474

• 0.526

• 0.720

• 1

Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (We will ignore the small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. What is the probability that a randomly chosen death was due to diabetes?

• 0.96

• 0.107

• 0.042

• 0.038

• 0.030

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. Which of the following is the conditional probability of A, given B?

• 1/2

• 3/10

• 1/5

• 1/6

• Cannot be determined from the information given.

In a large high school 15% of Sophomores, 25% of Juniors, and 55% of Seniors drive to school. According to the registration office 24% of students are Sophomores, 26% are Juniors, and 30% are Seniors. Suppose we select one student from this school at random and record which class they are in as well as whether they drive to school or not.

(a) Draw a tree diagram to model this random process.

In a large high school 15% of Sophomores, 25% of Juniors, and 55% of Seniors drive to school. According to the registration office 24% of students are Sophomores, 26% are Juniors, and 30% are Seniors. Suppose we select one student from this school at random and record which class they are in as well as whether they drive to school or not.

Find the probability that the student drives to school.

In a large high school 15% of Sophomores, 25% of Juniors, and 55% of Seniors drive to school. According to the registration office 24% of students are Sophomores, 26% are Juniors, and 30% are Seniors. Suppose we select one student from this school at random and record which class they are in as well as whether they drive to school or not.

Suppose the chosen person drives to school. What is the probability that he or she is a Senior?