It is known that $40\%$ of students wear spectacles. From a sample of $10$ students, calculate the probability that exactly $2$ students wear spectacles.

I tried $0.4^2 \cdot 0.6^8$, which is two students wear spectacles times $8$ students did not wear spectacles, where $0.6 = 1-0.4$.

But the answer is not correct.

  • 2
    $\begingroup$ Hi, welcome to StackExchange, it is expected that you tell us what you have tried in order to solve the problem rather than just typing up the problem with no attempts visible. Thanks $\endgroup$ – Aneesh Sep 28 '15 at 13:19
  • $\begingroup$ Hint: $any$ 2 students $\endgroup$ – Alex Sep 28 '15 at 13:28

You're leaving out the binomial coefficient term of the probability mass function when doing your calculation.

$Pr(X = k) = {n\choose k}p^k(1-p)^{n-k}$

Take what you have and multiply it by ${n\choose k}$.



What is $p\{X=2\}$ if $X$ follow a $\text{Binomial}(10,2/5)$ ?


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