Question

I only have 3 attempts to get this answer correct. HELP

a basketball player's three point shooting. Assume that his shots are Bernoulli trials, and that he makes 1 in 5 of his shots.

How many three point shots must the player attempt so that the probability of his hitting at least one of them is at least 0.94

Answer 1

The basketball player must attempt 12 shots to have a probability of at least 0.94 of hitting at least one of them.

Step-by-step explanation:

This is a Bernoulli trial problem, where the basketball player's shots can be considered as independent trials with a constant probability of success. The probability of the player making a shot is 1 in 5, or 0.2. We need to find the number of shots the player must attempt so that the probability of hitting at least one of them is at least 0.94.

To solve this, we can use the complement rule. The probability of not hitting any shot in a given attempt is 1 - 0.2 = 0.8. Therefore, the probability of not hitting any shot in n attempts is (0.8)n. We want this probability to be less than or equal to 0.06 (1 - 0.94), so we can set up the inequality:

(0.8)n ≤ 0.06

By taking the logarithm of both sides, we can solve for n:

n ≥ log0.8 (0.06) ≈ 11.94

Since we can't have a fraction of an attempt, we round up to the nearest integer. Therefore, the basketball player must attempt 12 shots in order to have a probability of at least 0.94 of hitting at least one of them.

Answer 2

Points make = 1/5, so Points miss = 4/5
for Points make to be ≥ 0.94, Points miss ≤0.06 in n trials

first set (4/5)^n = 0.06

taking logs,

n*log(4/5) = log 0.06

n = log 0.06/log(4/5) = 12.608, to be rounded

the answer is 13