10. Pick A Ball In the game of Pick-A-Ball, there are 10 colored balls: 2 red, 4

Question

10. Pick A Ball

In the game of Pick-A-Ball, there are 10 colored balls: 2 red, 4 white, and 4 blue. The balls have been placed into a small bucket, and the bucket has been shaken th Aplia: udent Question ked to reach into the bucket without looking and select 2 balls. Because the bucket has been shaken thoroughly, you can assume that each individual ball is selected at random with equal likelihood of being chosen. It is common in games of chance to be rewarded for obtaining unlikely results. For example, in the game of poker, hands that are less likely to occur tend to trump hands that are more likely to occur. That same concept applies in this game. It costs $10 to play Pick-A-Ball, and your prize is the reciprocal of the probability of obtaining your exact sequence of results, expressed in dollars. For example, if the probability of obtaining your exact sequence of results is 0.10, your prize is 1/0.10 $10, and you break even. Therefore, to make a positive profit from playing pick-A-Ball, the probability of obtaining your results must be lower than 0.10. When you reach into the bucket, your result is based on a simulation. In a simulation, random events are modeled in such a way that the simulated outcomes closely match real-world outcomes. In this simulation, your result is simulated based on the probabilities of obtaining a ball of a particular color. Now, close your eyes! Reach into the bucket, and pick a ball. (Click the red Pick-A-Ball! con to simulate reaching into the bucket and drawing your ball.) Pick-A-Ball!

Explanation / Answer

probabilty of picking a white ball=4/10=0.4

probabilty of picking a red ball in second turn =first ball red *second red+first ball not red*second red

=(2/10)*(1/9)+(8/10)*(2/9)=18/90=1/5=0.2

probabilty of getting exact sequence =(4/10)*(2/9)=8/90=0.0889

prize =1/0.0889=$11.25

profit=$11.25-$10=$1.25

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