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Chapter 3: Q. 3.29 (page 99)

There are 15 tennis balls in a box, of which 9 have not previously been used. Three of the balls are randomly chosen, played with, and then returned to the box. Later, another 3 balls are randomly chosen from the box. Find the probability that none of these balls has ever been used.

Short Answer

Expert verified

The likelihood is that none of these balls have ever been used is.0893

Step by step solution

01

Step1:Given data

Case 0: No used balls are drawn. p0=93153

Case 1:1used ball is drawn. p1=92路6153

Case2:2 used balls are drawn.p2=9路62153

Case3:3 used balls are drawn. p3=63153

02

Step2:Three of the balls are chosen at random.

Case 0:p0=.1846,6new balls, 9used left over.

Case 1:p1=.4747,7new balls,8used.

Case2:p2=.2967,8new balls,7used.

Case3:p3=.044,9 new balls, 6 used.

03

Another 3 ball is drawn at random from the box.

p063153+p173153+p283153+p393153

We multiply each case's probability by the probability that no used balls are found in the second draw, and then add it all up.

04

Step4:It's possible that none of these balls have ever been used.

.1846脳.044+.4747脳.0769+.2967脳.1231+.044脳.1846=.0893

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