Answer :

Given:

⇒ Bag contains 10 black balls and 8 red balls

It is told that two balls are drawn from bag with replacement.

Let us find the Probability of drawing each colour ball from the bag.

⇒ P(B_{1}) = P(drawing black ball from bag)

⇒

⇒

⇒

⇒ P(R_{1}) = P(drawing red ball from bag)

⇒

⇒

⇒

We need to find:

(i) P(D_{rr}) = P(both balls drawn are red)

(ii) P(D_{br}) = P(first drawn is black and next is red)

(iii) P(S_{rd}) = P(one ball is red and other is black)

⇒ P(D_{rr}) = P(both balls drawn are red)

Since drawing a ball is independent for each bag, the probabilities multiply each other.

⇒

⇒

⇒

⇒ P(D_{br}) = P(first drawn is black and next is red)

Since drawing a ball is independent for each bag, the probabilities multiply each other.

⇒

⇒

⇒

⇒ P(S_{rb}) = P(one ball is red and other is black)

⇒ P(S_{rb}) = P(first drawn is red and next is black) + P(first drawn black and next is red)

⇒ P(S_{rb}) = P(D_{rb}) + P(D_{br})

Since drawing a ball is independent for each bag, the probabilities multiply each other.

⇒

⇒

⇒

⇒

∴ The required probabilities are .

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