#### Question

The probability of selecting a male or a female is same. If the probability that in an office of *n* persons (*n* − 1) males being selected is \[\frac{3}{2^{10}}\] , the value of *n* is

##### Options

5

3

10

12

#### Solution

12

Let *X* be the number of males.

\[p = q = \frac{1}{2}\ (\text{ given} )\]

\[P(X = n - 1) = ^{n}{}{C}_{n - 1} \left( p \right)^{n - 1} q^1 = \frac{3}{2^{10}}\]

\[ \Rightarrow n \left( \frac{1}{2} \right)^n = \frac{3}{2^{10}} \]

\[ \Rightarrow n \left( \frac{1}{2} \right)^n = 3\left( \frac{2^2}{2^{12}} \right) \]

\[ \Rightarrow n \left( \frac{1}{2} \right)^n = 12 \left( \frac{1}{2} \right)^{12} \]

\[\text{ By comparing the two sides, we get n } = 12\]

Is there an error in this question or solution?

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The Probability of Selecting a Male Or a Female is Same. If the Probability that in an Office of N Persons (N − 1) Males Being Selected is 3 2 10 , the Value of N is Concept: Bernoulli Trials and Binomial Distribution.

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