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Conditional Probability & Bayes' Theorem · Question 105 of 125

What is the probability that the egg is cracked?

Question 105

MediumOriginal 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 cracked?

Options for question 105

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. P(C)=0.7×0.05+0.3×0.1P(C) = 0.7 \times 0.05 + 0.3 \times 0.1.

  2. 0.035+0.03=0.0650.035 + 0.03 = 0.065.

Worth noting

0.075 averages 5% and 10%, as if the farms sent equal numbers.

Concept
The theorem of total probability
Typical time
120 s
Your time
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The rule this testsBayes' theorem
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