Question

Seven hundred tickets will be sold and these will be raffled during the fiesta of Brgy. Masiete. One of these tickets will win ₱10,000 and the rest will win nothing. What will be the expected value and variance of your gain if you will buy one of the tickets?

Answer 1

Probability of win ticket is 1/700, not to win 699/700.

$$E(X)=\dfrac{1}{700}(10000)+\dfrac{699}{700}(0)=\dfrac{100}{7}\approx14.29$$

$$Var(X)=\sigma^2$$

$$=\dfrac{1}{700}(10000-\dfrac{100}{7})^2+\dfrac{699}{700}(0-\dfrac{100}{7})^2$$

$$\approx142653.06$$