GATE 2021 EC – Question 61
In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% 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.
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Correct answer: 3.30 to 3.34
Explanation
Let $P(\text{boy}|S)=b$. Then $P(\text{boy}|C)=2b$ and, since half the students are boys, $0.75b+0.25(2b)=0.5$, so $b=0.4$ and $P(\text{boy}|C)=0.8$, $P(\text{girl}|C)=0.2$. Then $P(C|\text{girl})=\frac{0.2\times0.25}{0.5}=0.1$. The information gained is $-\log_2 0.1=\log_210=3.32$ bits.