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)
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(SBR) = P(drawing Blue marble followed by Red)
Since drawing a marble is an independent event, the probabilities multiply each other
⇒ P(Sany) = P(drawing Blue and red marble in any order)
⇒ P(Sany) = 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 \(\cfrac{15}{64},\cfrac{15}{32},\cfrac{17}{32}.\)