When employees with smart phones are randomly | vedclass

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Question

(A) Let success be selecting a smart phone used for office purposes. Here,the probability of success $p = 50 \% = \frac{1}{2}$. The probability of fai

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${ }^{10} C_2 \frac{1}{2^{10}}$

Vedclass · Answer

(A) Let success be selecting a smart phone used for office purposes. Here,the probability of success $p = 50 \% = \frac{1}{2}$. The probability of failure $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$. We have $n = 10$ trials and we want exactly $r = 2$ successes. Using the Binomial distribution formula $P(X = r) = { }^n C_r p^r q^{n-r}$: $P(X = 2) = { }^{10} C_2 \cdot (\frac{1}{2})^2 \cdot (\frac{1}{2})^{10-2}$ $P(X = 2) = { }^{10} C_2 \cdot (\frac{1}{2})^2 \cdot (\frac{1}{2})^8$ $P(X = 2) = { }^{10} C_2 \cdot (\frac{1}{2})^{10} = { }^{10} C_2 \frac{1}{2^{10}}$.

When employees with smart phones are randomly selected,$50 \%$ use them for office purpose. The probability that out of $10$ users exactly $2$ of them use for office purpose is

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