An example Is given to 6 students to solve. The probability of ge… - Vidyadip

Question

An example Is given to $6$ students to solve. The probability of getting correct solution of the problem by any student is $0.6 .$ Students are trying to solve the problem independently. Find the probability of getting the correct solution by only $2$ out of the 6 students.

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Answer

Here, $n=6$
$x=$ No. of student getting correct solution of the problem $=2$
$p=$ Probability of getting correct solution of the problem $=0.6$
$\therefore q=1-p=1-0.6=0.4$
Putting, $n=6, x=2, p=0.6$ and $q=0.4$ in
$P(X=X)=p(x)={ }^n C_x p^x q^{n-x}$
$p(x)={ }^6 C_x(0.6)^x(0.4)^{6-x}$
$\therefore P(X=2)=p(2)={ }^6 C_2(0.6)^2(0.4)^{6-2}$
$=15(0.36)(0.4)^4$
$=15(0.36)(0.0256)$
$=0.13824$
Hence, the probability of getting the correct solution of the problem obtained is $0.13824 .$

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