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Conditional Probability & Bayes' Theorem · Question 121 of 125

The egg is not cracked.

Question 121

HardOriginal question

A shop gets 70% of its eggs from farm P and 30% from farm Q. Of P's eggs, 5% are cracked; of Q's, 10% are cracked. An egg is picked at random.

The egg is not cracked. What is the probability that it came from farm P?

Options for question 121

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. P(C′)=1−0.065=0.935P(C') = 1 - 0.065 = 0.935, and P(P∩C′)=0.7×0.95=0.665P(P \cap C') = 0.7 \times 0.95 = 0.665.

  2. P(P∣C′)=0.6650.935=133187P(P \mid C') = \frac{0.665}{0.935} = \frac{133}{187}.

Worth noting

0.95 is P(C′∣P)P(C' \mid P), the reverse conditional; the answer is only a little above P's share of 0.7.

Concept
Bayes' theorem
Typical time
150 s
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