In a carnival game, the player selects a ball one at a time, without replacement
ID: 3316168 • Letter: I
Question
In a carnival game, the player selects a ball one at a time, without replacement, from an urn containing three red ball and four white balls. The game proceeds until a red ball is drawn. The player pays $3.00 to play the game and receives $1.50 for each ball drawn. Write down the probability distribution for the player's earnings, and find its expected value.
Give the probability distribution. List the earnings from the smallest value to the largest value and type the probabilities as simplified fractions. Probability Earnings s-1.50 7 2 7 $0 $1.50 35Explanation / Answer
Let R = random variable representing the player's earnings for this game.
The elements of the sample space of drawings are {r, wr, wwr, wwwr, wwwwr}
The probability of the outcome r is 3/7. The earning is 1.50 - 3 = - 1.50
The probability of the outcome wr is 4/7 * 3/6 = 2/7. The earning is 0
The probability of the outcome wwr is 4/7 * 3/6 * 3/5 = 6/35. The earning 3 * 1.50 - 3 = 1.50
The probability of the outcome wwwr is 4/7 * 3/6 * 2/5 * 3/4 = 3/35. the earning is 4 * 1.50 - 3 = 3.00
The probability of the outcome wwwwr is 4/7 * 3/6 * 2/5 * 1/4 * 3/3 = 1/35. The earning is 5 * 1.50 - 3 = 4
Expected value = 3/7 * - 1.50 + 6/35 * 1.5 + 3/35 * 3 + 1/35 * 4 = - 0.0143