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Conditional Probability & Bayes' Theorem · Question 120 of 125

The egg is cracked. What is the probability that it came from farm Q?

Question 120

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 cracked. What is the probability that it came from farm Q?

Options for question 120

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. P(Q∣C)=P(Q∩C)P(C)=0.030.065P(Q \mid C) = \frac{P(Q \cap C)}{P(C)} = \frac{0.03}{0.065}.

  2. =3065=613= \frac{30}{65} = \frac{6}{13}.

Worth noting

713\frac{7}{13} is the chance it came from farm P.

Concept
Bayes' theorem
Typical time
150 s
Your time
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The rule this testsBayes' theorem
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