Answer to Question #95825 in Statistics and Probability for Carine

Question

Bruce pays $2 for the privilege of tossing a coin once. He will win $5 if heads shows up and will lose $3 if tails shows up. If the probability of heads on a toss is 0.6, find Bruce’s expected net winnings. In practical terms, how would you interpret the expected winnings?

Answer 1

$$p(H)=0.6,\ p(T)=0.4$$

For getting a head, the winning is $5 and for a tail, the loss is $3.

So X is a random variable that takes values 5 or -3 with probabilities 0.6 and 0.4 respectively.

Then

$$E(X)=5\cdot0.6+(-3)\cdot0.4=1.8$$

Since Bruce pays $2 for the privilege of tossing a coin once, then the expected winning will be

$$1.8-2=-0.2$$

In practical terms, the expected lose will be $0.2. Bruce should not play.