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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 - 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

 

Options
  • 5

  • 3

  • 10

  • 12

     

Solution

12
Let X be the number of males. 

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

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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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