Question

Mrs. Wheeler prepares a list of 43 U.S. Presidents, 31 of whom served in the military. Then, 8 students each select a president at random (with possible repeats) for their civics presentations. What is the probability that at least one of the students will select a president who did not serve in the military? Round your answer to the nearest hundredth.

a. 0.08
b. 0.21
c. 0.58
d. 0.79

Answer 1

To find the probability that at least one of the students will select a president who did not serve in the military, we can use the concept of complementary probability. The probability is approximately 0.08.

Step-by-step explanation:

To find the probability that at least one of the students will select a president who did not serve in the military, we can use the concept of complementary probability.

The complement of the event of at least one student selecting a president who did not serve in the military is the event of all students selecting presidents who served in the military.

We can calculate this probability using the rule of independent events. Since each student selects a president independently with possible repeats, the probability of each student selecting a president who served in the military is 31/43.

1. We calculate the probability of all students selecting presidents who served in the military, which is (31/43)8.
2. We subtract this probability from 1 to get the probability of at least one student selecting a president who did not serve in the military: 1 - (31/43)8.
3. Rounding this answer to the nearest hundredth, the probability is approximately 0.08.