Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisHard

At an animal shelter, 70%70\% of the animals are dogs and the rest are cats. Of the dogs, 20%20\% are younger than 11 year, and of the cats, 50%50\% are younger than 11 year. If an animal younger than 11 year is selected at random from the shelter, what is the probability that it is a cat?

A

320\frac{3}{20}

B

310\frac{3}{10}

C

12\frac{1}{2}

D

1529\frac{15}{29}

Show answer and explanation

Answer: D

Picture 100100 animals, 7070 dogs and 3030 cats. Then 0.20×70=140.20 \times 70 = 14 dogs and 0.50×30=150.50 \times 30 = 15 cats are younger than 11 year, which is 2929 young animals in all. The probability that a young animal is a cat is 1529\frac{15}{29}.

Choice C is the probability that a cat is younger than 11 year, but the question tells you the animal's age and asks about its species, so the denominator is all 2929 young animals.

Why the other choices are wrong

  • A. 3/20 is the probability that a randomly selected animal is a young cat, not the probability among young animals.
  • B. 3/10 is the share of all animals that are cats, which ignores the information about age.
  • C. 1/2 is the probability that a cat is young, which reverses the condition.
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