Question

A lottery ticket costs 10 dollars. You have a 2% chance to win 400 dollars, otherwise you win nothing. Write down a probability distribution table for the random variable X = net gain = (amount won)-(ticket cost), and nd its expected value (hint: answer is an integer). Should you play or not

Answer 1

When you win 400 dollars with probability = 0.02, Net Gain = 400 - 10 = 390

When you lose lottery with probability = 1 - 0.02 = 0.98, Net Gain = 0 - 10 = -10

The probability distribution table for the random variable X is,

X	P(X)
390	0.02
-10	0.98

Expected value = E(X) = $\sum X P(X)$

= 0.02 * 390 + 0.98 * -10

= -2

The expected value is -$2