In the game of Pick-A-Ball, there are 10 colored balls: 3 red,4 white, and 3 blu

Question

In the game of Pick-A-Ball, there are 10 colored balls: 3 red,4 white, and 3 blue. The balls have been placed into a small bucket, and the bucket has been shaken thoroughly. You will be asked 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 ess 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 ower 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 robabiliies 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-Balll icon to simulate reaching into the bucket and drawing your ball.)

Explanation / Answer

probability of selecting the color (white) of ball that you just selected =4/10=0.4

probabilityof selecting the  color (white) of ball that you just selected =3/9 =0.3333

probability of obtaining the ssequence =0.4*0.3333=0.1333

prize =1/0.1333 =$7.5

profit =7.5-10 = $ -2.50

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.