Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisHard

A survey asked 400400 adults whether they prefer streaming services or cable television. Of the 150150 adults under age 3030, 80%80\% prefer streaming. Of the 250250 adults age 3030 or older, 105105 prefer streaming. If one of the adults who prefer streaming is selected at random, what is the probability that the adult is under age 3030?

A

310\frac{3}{10}

B

715\frac{7}{15}

C

815\frac{8}{15}

D

45\frac{4}{5}

Show answer and explanation

Answer: C

Of the 150150 adults under 3030, 0.80×150=1200.80 \times 150 = 120 prefer streaming. In all, 120+105=225120 + 105 = 225 adults prefer streaming. If one of these 225225 adults is selected, the probability that the adult is under 3030 is 120225=815\frac{120}{225} = \frac{8}{15}.

Choice D is the probability that an adult under 3030 prefers streaming, which reverses the condition in the question.

Why the other choices are wrong

  • A. 3/10 is 120 out of all 400 adults, but the adult is selected only from the 225 who prefer streaming.
  • B. 7/15 is 105 out of 225, the probability that a streaming fan is 30 or older.
  • D. 4/5 is the probability that an adult under 30 prefers streaming, which reverses the condition.
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