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 A ?, box B?, box C?
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 A ?, box B?, box C?

Solution:

Let us assume R be the event of drawing the red marbles
Let us additionally assume that the letters E_{A}, E_{B} and E_{c} denote the boxes A, B and C respectively

Given that,

Total number of marbles =40

Also, total number of red marbles =15

P(R)=15 / 40

=3 / 8

Probability of taking out the red marble from box A,

P\left(E_{A} \mid R\right)=\frac{P\left(E_{A} \cap R\right)}{P(R)}

=\frac{\frac{1}{40}}{3}

=1 / 15

Also, probability of taking out the red marble from box B,

P\left(E_{B} \mid R\right)=\frac{P\left(E_{B} \cap R\right)}{P(R)}

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

=2 / 5

And, Probability of taking out the red marble from box \mathrm{C},

P\left(E_{C} \mid R\right)=\frac{P\left(E_{C} \cap R\right)}{P(R)}

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

=8 / 15