Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisMedium

A basketball player makes 80%80\% of her free throws, and the result of each free throw is independent of the others. If she attempts 22 free throws, what is the probability that she makes exactly 11 of them?

A

0.160.16

B

0.320.32

C

0.640.64

D

0.800.80

Show answer and explanation

Answer: B

She can make exactly 11 free throw in two ways. She can make the first and miss the second, with probability 0.8×0.2=0.160.8 \times 0.2 = 0.16, or miss the first and make the second, with probability 0.2×0.8=0.160.2 \times 0.8 = 0.16. The total probability is 0.16+0.16=0.320.16 + 0.16 = 0.32.

Choice A counts only one order, make then miss, but miss then make also gives exactly 11 made free throw.

Why the other choices are wrong

  • A. 0.16 counts only one order, make then miss. Miss then make also works, so double it.
  • C. 0.64 is the probability of making both free throws.
  • D. 0.80 is the probability of making a single free throw.
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