Bus Econ 3.1.54 Question Help In a carnival game, the player selects a ball one

Question

Bus Econ 3.1.54 Question Help In a carnival game, the player selects a ball one at a time, without replacement, from an urn containing two purple balls and four black balls. The game proceeds until a purple 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 Earnings Probability ext Enter your answer in the edit fields and then click Check Answer 2 parts remaining Clear All Final Check ction

Explanation / Answer

In the above table, we have listed the earning of player along with its probability. Here the probability is computed on the basis of number of black balls drawn before the first purple ball appears.

For 0 black ball drawn the first ball drawn is purple, which appears with probability 2/6 = 0.3333

For 1 black ball drawn, the first ball drawn is black and second is purple, probability = 4/6 * 2/5 = 0.2667

Similarly, probabilities are computed for 2, 3 and 4 black balls drwan before the first purple ball appears.

Earnings are calculated as amount recieved - amount paid.

No. of Black balls Drawn Player Pays Player Receives Earnings Probability 0 3 0 -3 0.3333 1 3 1.5 -1.5 0.2667 2 3 3 0 0.2000 3 3 4.5 1.5 0.1333 4 3 6 3 0.0667

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