Chapter 14.4, Problem 12E

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS3-12 ■ 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. To determine The expected value of the game. Explanation 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

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