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Question
A bag contains 3 red and 5 white balls. Two balls are drawn at random one after the other without replacement. Find the probability that both the balls are white.
Solution: Let,
A : First ball drawn is white
B : second ball drawn in white.
P(A) = `square/square`
After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining `square` balls.
∴ P(B/A) = `square/square`
∴ P(Both balls are white) = P(A ∩ B)
`= "P"(square) * "P"(square)`
`= square * square`
= `square`
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Solution
Let, A: First ball drawn is white
B: Second ball drawn is white.
P(A) = `underline(5/8)`
After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining 7 balls.
∴ `"P"("B"//"A")` = `underline(4/7)`
∴ P(Both balls are white) = P(A ∩ B)
= `"P"underline(("A")) * "P"underline(("B"//"A"))`
= `underline(5/8) . underline(4/7)`
= `underline(5/14)`
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