Given:

⇒ Bag A contains 3 red balls and 5 black balls

⇒ Bag B contains 6 red balls and 4 black balls

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

We need to find the probability that one ball is red and other is black.

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

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

⇒

⇒

⇒

⇒ P(R₁) = P(drawing Red ball from bag A)

⇒

⇒

⇒

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

⇒

⇒

⇒

⇒ P(R₂) = P(drawing Red ball from bag B)

⇒

⇒

⇒

We need to find the probability of drawing the different colour balls from two bags

⇒ P(S) = P(drawing one red ball and one Black ball)

⇒ P(S) = P(drawing black balls from bag A and red ball from bag B) + P(drawing black balls from bag B and red ball from bag A)

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

⇒

⇒

⇒

⇒ .

∴ The required probability is .