GATE EC 2021 Set 1 — Question 61
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Communications → Information Theory → Conditional Probability
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Question
In a high school having equal number of boy students and girl students, of the students study Science and the remaining students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is ________ bits.
Correct answer
3.32 to 3.325
Solution
Let and denote boy and girl students respectively. .
Let and denote Science and Commerce students respectively. .
Given: .
Using total probability:
.
Then .
We need the probability that a girl student studies Commerce, :
.
The amount of information gained is .
Let and denote Science and Commerce students respectively. .
Given: .
Using total probability:
.
Then .
We need the probability that a girl student studies Commerce, :
.
The amount of information gained is .
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