Given:

⇒ Bag A contains 4 white balls and 2 black balls

⇒ Bag B contains 3 white balls and 5 black balls

It is told that one ball is drawn is drawn from is each bag.

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

⇒ P(B₁) = P(drawing black ball from bag A)

⇒

⇒

⇒

⇒ P(W₁) = P(drawing white ball from bag A)

⇒

⇒

⇒

⇒ P(B₂) = P(drawing black ball from bag B)

⇒

⇒

⇒

⇒ P(W₂) = P(drawing white ball from bag B)

⇒

⇒

⇒

We need to find:

i. P(D_WW) = P(Both are white)

ii. P(D_BB) = P(Both are black)

iii. P(D_WB) = P(One drawn is white and other is black)

⇒ P(D_WW) = P(Both are White)

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

⇒

⇒

⇒

P(D_BB) = P(Both balls are black)

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

⇒

⇒

⇒

P(D_WB) = P(One ball drawn is white and other is black)

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

⇒

⇒

⇒

⇒ .

∴ The required probabilities are .