SKILLS

3-12 ■ Expected Value of a Game Find the expected value (or expectation) of the games described.

A bag contains eight white balls and two black balls. John picks two balls at random from the bag, and he wins $ 5 if he does not pick a black ball.

The expected value of the game.

Approach:

The formula for probability is given as,

p=n(E)n(S) ……(1)

Here, p is the probability, n(E) is the number of event and n(S) is the total number of sample.

The expected value is given as,

E=a1p1+a2p2+⋯+anpn ……(2)

Here, a1,a2,…,an is the amount of payout and p1,p2,…,pn is the probability of payout.

Given:

A bag contains 8 white balls and 2 black balls. John picks 2 balls at random from the bag, and he wins $5.

Calculation:

The total outcome is C(10,2).

Calculate the probability, if both the balls are white.

Substitute C(10,2) for n(S) and C(8,2) for n(E) in equation (1) to calculate the probability.

p1=C(8,2)C(10,2)=2845

Calculate the probability, if one ball is white and one ball is black