Question
A bag contains 6 white and 4 black balls . Two balls are drawn at random . Find he probability that they are of the same colour ..
Answer: Option D
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Let S be he sample space . Then
n (S) = Number of ways of drawing 2 balls out of (6 + 4) = `10_ (C _ 2) = ((10 xx 9))/((2 xx 1))` = 45.
Let (E) = Event of getting both balls of the same colour . Then ,
n (E) = Number of ways of drawing ( 2 balls out of 6) or ( 2 balls out of 4)
= `(6_ (C_ 2) + 4_ (C _ 2))`
=`((6 xx 5))/((2 xx 1)) + ((4 xx 3))/((2 xx 1))` = (15 + 6) = 21.
`:.` P (E) = ` (n(E))/(n(S)) = 21/45 = 7/15`
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