# 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 - Mathematics

#### 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

• 5

• 3

• 10

• 12

#### Solution

12
Let X be the number of males.

$p = q = \frac{1}{2}\ (\text{ given} )$
$P(X = n - 1) = ^{n}{}{C}_{n - 1} \left( p \right)^{n - 1} q^1 = \frac{3}{2^{10}}$
$\Rightarrow n \left( \frac{1}{2} \right)^n = \frac{3}{2^{10}}$
$\Rightarrow n \left( \frac{1}{2} \right)^n = 3\left( \frac{2^2}{2^{12}} \right)$
$\Rightarrow n \left( \frac{1}{2} \right)^n = 12 \left( \frac{1}{2} \right)^{12}$
$\text{ By comparing the two sides, we get n } = 12$

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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.