Question

A football quarterback has 2 more chances to throw a touchdown before his team is forced to punt the ball. He misses the receiver on the first throw 30% of the time. When his first throw is incomplete, he misses the receiver on the second throw 10% of the time.

Part A: What is the probability of not throwing the ball to a receiver on either throw? (5 points)

Part B: What is the probability of making at least 1 successful throw? (5 points)

Answer 1

Answer: Part A : 0.03
Part B : 0.97

Explanation:

Part A: The probability of not throwing the ball to a receiver on either throw can be calculated as follows:

• The probability of missing the receiver on the first throw is 30% or 0.3.

• The probability of missing the receiver on the second throw given that the first throw was incomplete is 10% or 0.1.

Therefore, the probability of not throwing the ball to a receiver on either throw is:

P(missed on both throws) = P(missed on first throw) * P(missed on second throw given that first throw was incomplete)

= 0.3 * 0.1

= 0.03

Part B: The probability of making at least one successful throw can be calculated as follows:

• The probability of making at least one successful throw is equal to one minus the probability of missing both throws.

P(at least one successful throw) = 1 - P(missed on both throws)

= 1 - 0.03

= 0.97

Therefore, the probability of making at least one successful throw is 0.97.