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13 September, 00:52

Two balls are drawn in succession out of a box containing 4 red and 3 white balls. Find the probability that at least 1 ball was red, given that the first ball was (A) Replaced before the second draw. (B) Not replaced before the second draw.

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  1. 13 September, 03:32
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    A) 40/49

    B) 36/42

    Step-by-step explanation:

    Given:

    Red Balls, R : 4

    White Balls, W : 3

    Total Balls : 3+4=7 balls

    A) If balls were replaced before the 2nd draw

    P (White) = 3/7; P (Red) = 4

    P (at least 1 red ball),

    = 1 - P (no red balls)

    = 1 - P (White, White)

    = 1 - (3/7) (3/7)

    = 1 - (9/49)

    = 40/49

    A) If balls were replaced before the 2nd draw

    P (1st White Ball) = 3/7; P (2nd White Ball) = 2/6

    P (at least 1 red ball),

    = 1 - P (no red balls)

    = 1 - P (1st White, 2nd White)

    = 1 - (3/7) (2/6)

    = 1 - 6/42

    = 36/42
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