Answer to Question #200729 in Statistics and Probability for adrian

Question

A small-time bingo card costs P100.00 for 5 games. The prize for the first three games is P5,000.00, the fourth is P10,000.00 and the last prize is P20,000.00. If 1,000 bingo cards are going to be sold and you could only win once, what is the expected value of a ticket?

Answer 1

Probability of the prize P5,000.00:

$p_1=\frac{1}{1000}\cdot\frac{3}{5}=\frac{3}{5000}$

Probability of the prize P10,000.00:

$p_2=\frac{1}{1000}\cdot\frac{1}{5}=\frac{1}{5000}$

Probability of the prize P20,000.00:

$p_3=\frac{1}{1000}\cdot\frac{1}{5}=\frac{1}{5000}$

The expected value of a ticket:

$E(X)=100\cdot0.999+(100-5000)\cdot3/5000+(100-10000)\cdot1/5000$

$+(100-20000)\cdot1/5000=99.9-\frac{44500}{5000}=99.9-8.9=P\ 91$