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Conditional Probability & Bayes' Theorem · Question 25 of 125

Given that the student does not study Physics, what is the probability that the student is a girl?

Question 25

MediumOriginal question

A group of 60 students has 36 girls and 24 boys. Of the girls, 20 study Physics; of the boys, 8 study Physics. One student is picked at random from the group.

Given that the student does not study Physics, what is the probability that the student is a girl?

Options for question 25

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Not Physics: 36−20=1636 - 20 = 16 girls and 24−8=1624 - 8 = 16 boys, 32 students in all.

  2. 16 of the 32 are girls: 1632=12\frac{16}{32} = \frac{1}{2}.

Worth noting

49=1636\frac{4}{9} = \frac{16}{36} is the chance that a girl does not study Physics; the condition here is not studying Physics, so divide by 32.

Concept
Conditional probability by counting
Typical time
120 s
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The rule this testsConditional probability
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