3. (3 points) Johnny and Dave play a game. In this ga This $10 is not recoverabl

Question

3. (3 points) Johnny and Dave play a game. In this ga This $10 is not recoverable. The box contains 50 balls of which 40 are Black, 5 are Red, 4 are Green and 1 is White. If Johnny draws a Black ball he wins nothing. He is out his $10 If Johnny draws a Red ball, he wins his $10 back. He is now even. If Johnny draws a Green ball, he wins $40. He is now up $30. If Johnny draws the White ball, he wins $250. He is now up $240. Let X be the amount Johnny wins or loses after playing the game. a.) Create a probability distribution for X and find the expected value of X. b.) In whose favor is this game and why?

Explanation / Answer

probability of losing 10 dollar =P(X=-10)=P( of black ball)=40/50=0.8

probability of even =P(X=0)=P( of red ball)=5/50=0.1

probability of winning $30 =P(X=30)=P( of green ball)=4/50=0.08

probability of winning $240 =P(X=240)=P( of green ball)=1/50=0.02

below is probability distribution :

from above expected value = $-0.80

b) as expected value is negative this game is favourable to Dave.

x p(x) xP(x) -10 0.8000 -8.000 0 0.1000 0.000 30 0.0800 2.400 240 0.0200 4.800 total 1 = -0.80

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