You have a box full of washers that all have a one-inch outer diameter. Some are

Question

You have a box full of washers that all have a one-inch outer diameter. Some are of type A (a hole of half-inch diameter in the center), and some are of type B (a hole of quarter-inch diameter in the center).

a.The box contains 10washers of type A and 10washers of type B. Four washers are taken at random. What is the probability that the four washers are made up of two washers of type A and two washers of type B?

b.The box contains 100 washers of type A and 100 washers of type B. Four washers are taken at random. What is the probability that the four washers are made up of two washers of type A and two washers of type B?

c.The box contains 1000 washers of type A and 1000 washers of type B. Four washers are taken at random. What is the probability that the four washers are made up of two washers of type A and two washers of type B?

d.What happened to the probabilities? What did you expect? Why did you expect that?

Explanation / Answer

a) Probability = 10C2* 10C2/ 20C4 = 45*45/[20*19*18*17/24]=0.4179

b) Probability = 100C2 *100C2/[200C4]= 4950*4950/[ 200*199*198*197/24]=0.3787

c) Probability = 1000C2*1000C2 / 2000C4 = 1000*999/2*1000*99/2*1996!*4! /[2000!] 0.37537

We expected probability to derease in each case and stabilize around a critical vlue, like it has almost stabilized to 0.375 near the 3rd case

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