Q. 12.     Suppose we have four boxes A,B,C and D containing coloured marbles as given below:

                

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from  box B?

                

Answers (1)

Let R be event of drawing red marble.

Let E_A,E_B,E_C  respectivly denote event of selecting box A,B,C.

Total marbles = 40

Red marbles =15

    P(R)=\frac{15}{40}=\frac{3}{8}

Probability of drawing red marble from box B  is P(E_B|R)

                          P(E_B|R)=\frac{P(E_B\cap R)}{P(R)}

                                               =\frac{\frac{6}{40}}{\frac{3}{8}}

                                              =\frac{2}{5}

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