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A bag contain 3 white and 5 black balls. if 2 balls are drawn in succession without replacement, what is the probability that both are black

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Answer:

1328

Step-by-step explanation:

Use theory of conditional probability, we know that

P(X|Y)=P(X,Y)P(Y)

So, P(X,Y)=P(X|Y)P(Y)

Here let X1 be the event that the first ball drawn is white and let X2 be the event that second ball drawn is also white.

We want to find the joint probability P(X1,X2).

So, P(X1=W,X2=W)=P(X2=W|X1=W)P(X1=W)

P(X2=W|X1=W)=47

P(X1=W)=58.

So, P(X1,X2)=2056

Similarly now let Xi's represent events of both the balls being black.

Using the same calculation for black balls P(X1,X2)=656

So, the probability of both the balls have the same colour is

P(X1=W,X2=W)+P(X1=B,X2=B)=2056+656=1328

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