Question

1. Are the following events mutually exclusive?

Event A: Randomly selecting a male student at Riverdale High School.
Event B: Randomly selecting a member of the football team at Riverdale High School.

a. No, these are not mutually exclusive events
b. Yes, these are mutually exclusive events.

2. Use the Multiplication Rule to find the probability: The probability of a kidney transplant surgery is successful is 0.775. Find the probability of at least one surgery, out of 3, will be successful.

a. 0.997
b. 0.465
c. 0.535
d. 0.989

Answer 1

Explanation:

a. No, these are not mutually exclusive events because it is possible for a male student at Riverdale High School to be a member of the football team.

Using the Multiplication Rule, we can find the probability of at least one successful surgery out of three surgeries as follows:

P(at least one successful surgery) = 1 - P(no successful surgeries)

To find the probability of no successful surgeries, we use the complement rule and multiply the probabilities of three unsuccessful surgeries:

P(no successful surgeries) = 0.225 x 0.225 x 0.225 = 0.011390625

Therefore, the probability of at least one successful surgery out of three surgeries is:

P(at least one successful surgery) = 1 - 0.011390625 = 0.988609375

So, the answer is d. 0.989 (rounded to three decimal places).