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There are 4 white balls,4 red balls and 2 black balls in a bag,now take 4 balls

ID: 3174825 • Letter: T

Question

There are 4 white balls,4 red balls and 2 black balls in a bag,now take 4 balls from the bag,compute the probability in following cases. There are 4 white balls,4 red balls and 2 black balls in a bag,now take 4 balls from the bag,compute the probability in following cases (a) there are exactly 2 white balls in the 4 balls in the case that sampling with replacement and without ordering. (b) there are exactly 2 white balls in the 4 balls in the case that sampling without replacement and without ordering. (c) the 4 balls' sequence is white,red,black,black in the case that sampling with replacement and with ordering. (d) the 4 balls' sequence is white,red,black,black in the case that sampling without replacement and with ordering.

Explanation / Answer

a)

4 balls with replacement can be drawn in 10^4 ways

Required probability = (4C1 * 4C1 * 6C1 *6C1) / 10^4 = 0.0576

b)

4 balls without replacement can be drawn in 10C4 ways

Required probability = (4C2 *6C1) / 10C4 = 0.171

c)

Required sequence can be drawn in 4C1 * 4C1 * 2C1 *2C1

Total possible outcomes are 10^4

Required probability = (4C1 * 4C1 * 2C1 *2C1)/10^4 = 0.0064

d)

Required sequence can be drawn in 4C1 * 4C1 * 2C1 *1C1

Total possible outcomes are 10C4

Required probability = (4C1 * 4C1 * 2C1 *1C1)/10C4 = 0.152