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    Subject

    Quantitative Aptitude

    Topic

    Probability

    A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

    ক)
    23/42
    খ)
    19/42
    গ)
    7/32
    ঘ)
    16/39

    Explanation

    A red ball can be drawn in two mutually exclusive ways (i) Selecting bag I and then drawing a red ball from it. (ii) Selecting bag II and then drawing a red ball from it. Let E1, E2 and A denote the events defined as follows: E1 = selecting bag I, E2 = selecting bag II A = drawing a red ball Since one of the two bags is selected randomly, therefore P(E1) = 1/2  and  P(E2) = 1/2 Now, P(AE1)P\left(\frac A{E_1}\right) = Probability of drawing a red ball when the first bag has been selected = 4/7 P(AE2)P\left(\frac A{E_2}\right) = Probability of drawing a red ball when the second bag has been selected = 2/6 Using the law of total probability, we have P(red ball) = P(A) =  P(E1)×P(AE1)+P(E2)×P(AE2)P\left(E_1\right)\times P\left(\frac A{E_1}\right)+P\left(E_2\right)\times P\left(\frac A{E_2}\right) =  12×47+12×26=1942\frac12\times\frac47+\frac12\times\frac26=\frac{19}{42}

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