Answer :

Given:

Bag contains 3 blue and 5 red marbles

It is told that two marbles are drawn with replacement

Let us find the probability of drawing each marble from bag

⇒ P(B) = P(Drawing a Blue Marble)

⇒

⇒

⇒ P(R) = P(Drawing a Red Marble)

⇒

⇒

We need to find the probability that the marbles drawn:

i. Blue followed by red

ii. Blue and red in any order

iii. Of the same colour

⇒ P(S_{BR}) = P(drawing Blue marble followed by Red)

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

⇒

⇒

⇒

⇒ P(S_{any}) = P(drawing Blue and red marble in any order)

⇒ P(S_{any}) = P(drawing Blue marble followed by red) + P(drawing Red marble followed by Blue)

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

⇒

⇒

⇒

⇒ .

⇒ P(S) = P(drawing two marbles of same colour)

⇒ P(S) = P(drawing black balls from each bag) + (P(drawing white balls from each bag)

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

⇒

⇒

⇒

⇒ .

∴ The required probabilities are .

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