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5. There are two groups of subjects one of which contains 5 science subjects and 3 engineering subjects and the other consists of 3 science and 5 engineering subjects. An unbiased die is cast. If the number 3 or number 5 turns up, a subject is selected at random from the first group, otherwise the subject is selected at random from the second group. Find the probability that an engineering subject is selected ultimately.

  • maths -

    Engineering -- E
    Science ------ S

    Prob (E is picked from 1st group) = 3/8
    prob(E is picked from the 2nd group) = 5/8

    first picking is determined by a die toss of 3 or 5
    which has a prob of 2/6 or 1/3
    2nd picking is determined by any other die toss
    which is 2/3

    prob of your stated event
    = (1/3)(3/8) + (2/3)(5/8)
    = 3/24 + 10/24
    = 13/24

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