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Math Help - Probability

  1. #1
    Junior Member
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    Probability

    There are many marbles in a big box. It is known that 30% of the marbles are red, 60% are blue and the remaining 10% is not coloured.

    (a) A sample of 5 marbles is picked from the box. Find the probability that this sample contains not more than 2 red marbles.

    (b) Given that there are 4 coloured marbles (red or blue) in the sample, find the probability that the majority of the marbles in the sample is red.

    I managed to solve (a) but how do you solve (b)???

    This is conditional probability isn't it?

    Thanks for your help.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by cyt91 View Post
    There are many marbles in a big box. It is known that 30% of the marbles are red, 60% are blue and the remaining 10% is not coloured.

    (a) A sample of 5 marbles is picked from the box. Find the probability that this sample contains not more than 2 red marbles.

    (b) Given that there are 4 coloured marbles (red or blue) in the sample, find the probability that the majority of the marbles in the sample is red.

    I managed to solve (a) but how do you solve (b)???

    This is conditional probability isn't it?

    Thanks for your help.
    For (b), yes it's a conditional probability.

    Let X be the random variable of the number of coloured balls drawn in the sample where X~B(5 , 0.9)

    P(X=4)=5C4 x (0.9)^4 x (0.1) = 0.32805

    Let Y be the random variable of the number of red balls drawn where Y~B(4 , 0.3)

    In the sample of 4, there must be 3 or 4 red balls in order for it to be the majority.

    P(Y)=P(Y=3)+P(Y=4)

    =(0.3)^4 + 4C3 x (0.3)^3 x (0.7)

    = 0.0837

    Then the required probability would be 0.0837/0.32805=0.2551
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