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  • Suppose 10,000 tickets are sold in a lottery each for Re 1. First prize is of Rs 3000 and the second prize is of Rs. 2000. There are three third prizes of Rs. 500 each. If you buy one ticket, what is your expectation.

Suppose 10,000 tickets are sold in a lottery each for Re 1. First prize is of Rs 3000 and the second prize is of Rs. 2000. There are three third prizes of Rs. 500 each. If you buy one ticket, what is your expectation.

Answers (1)

Let X be the variable for the prize

The possibility is of winning nothing, Rs 500, Rs 2000 and Rs 3000.

So, X will take these values.

Since there are 3 third prizes of 500, the probability of winning third prize is \frac{3}{10000} .
1 first prize of 3000, so probability of winning third prize is \frac{1}{10000} .
1 second prize of 2000, so probability of winning third prize is \frac{1}{10000} .

\begin{aligned} &\begin{array}{|l|l|l|l|l|} \hline \mathrm{X} & 0 & 500 & 2000 & 3000 \\ \hline \mathrm{P}(\mathrm{X}) & \frac{9995}{10000} & \frac{3}{10000} & \frac{1}{10000} & \frac{1}{10000} \\ \hline \end{array}\\ &\text { since, } E(X)=X(P X)\\ &\text { Therefore, }\\ &\mathrm{E}(\mathrm{X})=0 \times \frac{9995}{10000}+\frac{1500}{10000}+\frac{2000}{10000}+\frac{3000}{10000}\\ &=\frac{1500+2000+3000}{10000}\\ &=\frac{6500}{10000}\\ &=\frac{13}{20}=\mathrm{Rs} 0.65 \end{aligned}

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