Question

A box contains 4 red and 6 black balls. Two balls are selected one after the other,

a) What is the probability that the first ball selected is black and the second ball selected is also black, if the selection is done without replacement.

b) What is the probability that the first ball selected is black and the second ball selected is red, if the selection is done without replacement.

c) What is the probability that the first ball selected is red and the second ball selected is black, if the selection is done with replacement.

Answer #1

a)

here two ball are drawn randomly one by one with replacement and there are 4 red and 6 black balls in the box

So if we want the probability such that both the balls are black then

1st ball drawn black with probability 6/10 and then second ball drawn with probabilty 5/9

since it is the case of without replacement

So the probabilty is

b)

similarly for this part probability is

C)

If it is with replacement then it will be

because here after the first draw the ball will be putted back to the box so there will be 10 ball in total for the second draw.

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