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Binomial Probability Issue!?

During winter it rains on average 18 out of 30 days. Five winter days are selected at random. Find, correct to four decimal places, the probabiity that:

a) the first two days chosen will be fine and the remainder wet,

b) more rainy days than fine days have been chosen

Update:

@ Bail Out

thanks for the attempt, that's basically what I have been doing the entire time. According to the back of the book, the answer to a) is 0.0124 and b) 0.7102

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    Let X days among the selected 5 days be wet.

    Then, X ~ B(n=5, p=18/30=0.6)

    p(x) = 5Cx*0.6^x*0.4^(5-x), x=0,1,2,3,4,5

    a) P[the first two days chosen will be fine and the remainder wet]

    = 12/30*12/30*18/30*18/30*18/30

    b) P[more rainy days than fine days have been chosen]

    = P[X > 5-X]

    = p(3) + p(4) + p(5)

    Hope this helps

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