Question

a basketball player hits three - point shots 43% of the time. if she takes 4 shots during a game, what is the probability that she hits all 4 shots?
a. 3.4%
b. 10.8%
c. 86%
d. 43%

Explanation:

Step1: Convert percentage to decimal

The probability of hitting a single shot \(p = 0.43\).

Step2: Use the multiplication rule for independent events

Since the shots are independent, the probability of hitting all 4 shots is \(p\times p\times p\times p=p^{4}\).
Substitute \(p = 0.43\) into the formula: \(0.43^{4}=0.43\times0.43\times0.43\times0.43\).
\(0.43\times0.43 = 0.1849\), \(0.1849\times0.43=0.079507\), \(0.079507\times0.43 = 0.03418801\approx0.034 = 3.4\%\)

Answer:

A. 3.4%