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Math Help - probability of urns

  1. #1
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    probability of urns

    An urn contains 3 red balls and 3 green balls. A ball is drawn randomly. If red, kept out. If green, returned to urn. Second ball is drawn, repeat. What is the probability that the urn contains exactly 4 balls after 3 are drawn?
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  2. #2
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    Quote Originally Posted by mhitch03 View Post
    An urn contains 3 red balls and 3 green balls. A ball is drawn randomly. If red, kept out. If green, returned to urn. Second ball is drawn, repeat. What is the probability that the urn contains exactly 4 balls after 3 are drawn?

    This is exactly as asking what's the probbly of drawing exactly 2 red balls in three intents. Let us denote B_i the ball drawn in the i-th intent.

    We have the following drawings that'll give 4 balls after 3 drawings:

    B_1=Red , B_2=Red, B_3=Green
    B_1=Red , B_2=Green , B_3=Red
    B_1=Green , B_2=Red , B_3=Red

    Now evaluate each event's probability. For example, in the first event the probability is \frac{1}{2}\cdot\frac{2}{5}\cdot\frac{3}{4}...can you see why?

    Tonio
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