Question

Suppose 10000 tickets are sold in a lottery each for $₹ 1$. First prize is of $₹ 3000$ and the second prize is of $₹ 2000$. There are three third prizes of $₹ 500$ each. If you buy one ticket, then your expectation is

• A. ₹ $0.61$
• B. ₹ $0.60$
• C. ₹ $0.65$
• D. ₹ $0.64$

Answer 1

Answer: (C)

Let $X$ denote the random variable of the prizes.
$\therefore X$ can take values $3000,2000,500$
$ P(X=3000)=\frac{1}{10000} $
$ P(X-2000)=\frac{1}{10000} $\
$ P(X=500)=\frac{3}{10000}$
Now, $\quad E(X)=\Sigma X P(X)$
$=3000 \times \frac{1}{10000}+2000 \times \frac{1}{10000} +500 \times \frac{3}{10000} $
$ =\frac{3000+2000+1500}{10000} $
$ =\frac{6500}{10000}=0.65$