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(D) Let $p$ be the probability that a student is good at mathematics, so $p = 0.6 = \frac{3}{5}$.Let $q$ be the probability that a student is not good

Vedclass · Accepted Answer

$\frac{2^8 	imes 3^2 	imes 7}{5^8}$

Vedclass · Answer

(D) Let $p$ be the probability that a student is good at mathematics, so $p = 0.6 = \frac{3}{5}$.Let $q$ be the probability that a student is not good at mathematics, so $q = 1 - 0.6 = 0.4 = \frac{2}{5}$.For a group of $n = 8$ students, the probability of having exactly $X = 2$ students good at mathematics follows the binomial distribution formula $P(X=k) = { }^n C_k 	imes p^k 	imes q^{n-k}$.Substituting the values: $P(X=2) = { }^8 C_2 	imes (0.6)^2 	imes (0.4)^6$.$P(X=2) = \frac{8 	imes 7}{2} 	imes \left(\frac{3}{5}ight)^2 	imes \left(\frac{2}{5}ight)^6$.$P(X=2) = 28 	imes \frac{3^2}{5^2} 	imes \frac{2^6}{5^6} = (2^2 	imes 7) 	imes \frac{3^2 	imes 2^6}{5^8} = \frac{2^8 	imes 3^2 	imes 7}{5^8}$.

If the probability that a student selected at random from a particular college is good at mathematics is $0.6$, then the probability of having exactly two students who are good at mathematics in a group of $8$ students of that college is:

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