A die is thrown 100 times. If the success is in getting an even number, then the variance of number of…

A die is thrown 100 times. If the success is in getting an even number, then the variance of number of successes is
  1. $1.10$
  2. $25$
  3. 50
  4. 100

Solution

This is an example of a binomial distribution.
Let \(\mathrm{A}\) be the event of obtaining an even number when a fair dice is thrown.
\(\begin{aligned}
& \therefore \mathrm{p}_{\mathrm{A}}=\frac{1}{2} \\
& \therefore \mathrm{p}_{\mathrm{A}^{\mathrm{c}}}=1-\mathrm{p}_{\mathrm{A}}=\frac{1}{2}
\end{aligned}\)
Variance over 100 trials \(=n \mathrm{p}_{\mathrm{A}} \mathrm{p}_{\mathrm{A}^{\mathrm{c}}}=100 \times \frac{1}{4}=25\)

Asked in: MHT CET 2020 (20 Oct Shift 1)

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