Question

5. Jacob makes 40% of the three-point shots he attempts. For a warm up, Jacob likes to shoot three-point shots until he makes one. Let M be the number of shots it takes Jacob to make his first three-point shot. Assume that the results of each shot are independent. Find the probability that it takes Jacob fewer than 4 attempts to make his first s

Answer 1

The probability that it takes Jacob fewer than 4 attempts to make his first three-point shot is 94.4%.

Step-by-step explanation:

To find the probability that it takes Jacob fewer than 4 attempts to make his first three-point shot, we need to calculate the probability of making the shot in 1, 2, or 3 attempts.

The probability of making the shot in 1 attempt is 40%. Therefore, the probability of not making the shot in 1 attempt is 60%.

The probability of making the shot in 2 attempts is (40% of 60%), or 24%. Therefore, the probability of not making the shot in 2 attempts is 76%.

The probability of making the shot in 3 attempts is (40% of 76%), or 30.4%. Therefore, the probability of not making the shot in 3 attempts is 69.6%.

Now we can calculate the total probability of making the shot in fewer than 4 attempts: 40% + 24% + 30.4% = 94.4%.