A man draws 3 balls from a jug containing 5 white balls and 7 black balls. He gets Rs. 20 for each white ball and Rs. 10 for each black ball. What is his expectation?Rs. 21.25Rs. 42.50Rs. 31.25Rs, 45.21
Question
A man draws 3 balls from a jug containing 5 white balls and 7 black balls. He gets Rs. 20 for each white ball and Rs. 10 for each black ball. What is his expectation?Rs. 21.25Rs. 42.50Rs. 31.25Rs, 45.21
Solution
The expectation or expected value in a probability problem is calculated by multiplying each possible outcome by the probability of that outcome, then adding those values.
First, we need to calculate the probability of drawing a white ball and a black ball.
The total number of balls is 5 (white) + 7 (black) = 12 balls.
The probability of drawing a white ball is 5/12 and for a black ball is 7/12.
The expected gain for a white ball is the product of the gain and the probability, which is Rs. 20 * 5/12 = Rs. 8.33.
Similarly, the expected gain for a black ball is Rs. 10 * 7/12 = Rs. 5.83.
The total expectation is the sum of these two expectations, which is Rs. 8.33 + Rs. 5.83 = Rs. 14.16.
So, the man can expect to gain Rs. 14.16 for each ball he draws. Since he draws 3 balls, his total expected gain is Rs. 14.16 * 3 = Rs. 42.48.
The closest answer to this is Rs. 42.50.
Similar Questions
An urn contains 5 white and 8 white black balls.Two successive drawing of three balls at a time aremade such that the balls are not replaced before thesecond draw. Find the probability that the first drawgives 3 white balls and second draw gives 3 blackballs.
A bag contains 5 white and 4 black balls. If 3 balls are drawn at random, what are theprobabilities of the following?(i) 2 of them are white? Ans : 10/21(ii) at most one of them is white Ans: 17/42(ii) at least two are white. Ans : 25/42
Ravi has a bag with 8 balls numbered 1 through 8. He is playing a game of chance.This game is this: Ravi chooses one ball from the bag at random. He wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. He loses $14 if 7 or 8 is selected.(If necessary, consult a list of formulas.)(a) Find the expected value of playing the game.dollars(b) What can Ravi expect in the long run, after playing the game many times?(He replaces the ball in the bag each time.)Ravi can expect to gain money.Hecanexpecttowindollarsperselection.Ravi can expect to lose money.Hecanexpecttolosedollarsperselection.Ravi can expect to break even (neither gain nor lose money).
ve balls are drawn from a bag containing6 white and 4 black balls. What; is theprobability that 3 are white and 2 black ?
Find the Expected value of the following distributionx -20 -10 30 75 80P(x) 3/20 1/5 1/2 1/10 1/20(a) 20.5(b) 21.5(c) 22.5(d) 24.5
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.