In a classroom, 5 % of the boys and 2 % of th | vedclass

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(D) Let $B$ be the event that the student is a boy and $G$ be the event that the student is a girl. Let $T$ be the event that the student is taller th

Vedclass · Accepted Answer

$\frac{4}{125}$

Vedclass · Answer

(D) Let $B$ be the event that the student is a boy and $G$ be the event that the student is a girl. Let $T$ be the event that the student is taller than $1.6 \ m$.Given: $P(G) = 0.60$, so $P(B) = 1 - 0.60 = 0.40$.Probability of a boy being taller than $1.6 \ m$: $P(T|B) = 5 \% = 0.05 = \frac{5}{100}$.Probability of a girl being taller than $1.6 \ m$: $P(T|G) = 2 \% = 0.02 = \frac{2}{100}$.Using the Law of Total Probability:$P(T) = P(B) \cdot P(T|B) + P(G) \cdot P(T|G)$$P(T) = 0.40 \cdot 0.05 + 0.60 \cdot 0.02$$P(T) = 0.020 + 0.012 = 0.032$$P(T) = \frac{32}{1000} = \frac{4}{125}$.

In a classroom, $5 \%$ of the boys and $2 \%$ of the girls are taller than $1.6 \ m$. The class consists of $60 \%$ girl students. The probability that a randomly selected student is taller than $1.6 \ m$ is:

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