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Conditional Probability & Bayes' Theorem · Question 100 of 125

What is the probability that the egg is from farm Q and cracked?

Question 100

EasyOriginal 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.

What is the probability that the egg is from farm Q and cracked?

Options for question 100

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. P(Q∩C)=P(Q) P(C∣Q)P(Q \cap C) = P(Q)\,P(C \mid Q).

  2. 0.3×0.1=0.030.3 \times 0.1 = 0.03.

Worth noting

0.1 is P(C∣Q)P(C \mid Q), the rate within Q's eggs, not the share of all eggs.

Concept
The multiplication theorem
Typical time
90 s
Your time
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The rule this testsBayes' theorem
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