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  • Question
  • 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.


  • Options
  • A. 23/42
  • B. 19/42
  • C. 7/32
  • D. 16/39

  • Correct Answer
  • 19/42 

    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 A E 1  = Probability of drawing a red ball when the first bag has been selected = 4/7

       P A E 2   = 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 E 1 × P A E 1 + P E 2 × P A E 2  

     

                              =  1 2 × 4 7 + 1 2 × 2 6 = 19 42

  • Tags: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO

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