Given:

Urn contains 7 red and 4 blue balls

It is told that two balls are drawn with replacement

Let us find the probability of drawing each marble from bag

⇒ P(B) = P(Drawing a Blue Ball)

⇒

⇒

⇒

⇒ P(R) = P(Drawing a Red Ball)

⇒

⇒

⇒

We need to find the probability that the balls drawn:

i. Both in red colour

ii. Both in blue colour

iii. One red and one blue

⇒ P(S_RR) = P(drawing Two red colour balls)

Since drawing a ball is an independent event, the probabilities multiply each other.

⇒

⇒

⇒

⇒ P(S_BB) = P(drawing two blue colour balls)

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

⇒

⇒

⇒

⇒ P(S_any) = P(drawing Blue and red ball in any order)

⇒ P(S_any) = P(drawing Blue ball followed by red) + P(drawing Red ball followed by Blue)

Since drawing a ball is an independent event, the probabilities multiply each other.

⇒

⇒

⇒

⇒ .

∴ The required probabilities are .