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Question
A bag contains 4 blue and 5 green balls. Another bag contains 3 blue and 7 green balls. If one ball is drawn from each bag, what is the probability that two balls are of the same colour?
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Solution
Let A be the event that a blue ball is drawn from each bag.
Probability of drawing one blue ball out of 4 blue balls where there are a total of 9 balls in the first bag and that of drawing one blue ball out of 3 blue balls where there are a total of 10 balls in the second bag is
P(A) = `4/9xx3/10`
Let B be the event that a green ball is drawn from each bag.
Probability of drawing one green ball out of 5 green balls where there are a total of 9 balls in the first bag and that of drawing one green ball out of 7 green balls where there are a total of 10 balls in the second bag is
P(B) = `5/9xx7/10`
Since both, the events are mutually exclusive and exhaustive events
∴ P(that both the balls are of the same colour)
= P(both are of blue colour) or P(both are of green colour)
= P(A) + P(B)
= `4/9xx3/10+5/9xx7/10`
= `12/90+35/90`
= `47/90`
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