Question

Suppose we have four boxes A, B, C, D containing coloured marbles as given below:
Figure

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?

Answer 1

Let R be the event of drawing the red marble.

Let E_A, E_B and E_C denote the events of selecting box A, box B and box C, respectively.

Total number of marbles = 40

Number of red marbles = 15

\[\therefore P\left( R \right) = \frac{15}{40} = \frac{3}{8}\]

Probability of drawing a red marble from box A is given by P(E_A/R).

\[\therefore P\left( E_A /R \right) = \frac{P\left( E_A \cap R \right)}{P\left( R \right)} = \frac{\frac{1}{40}}{\frac{3}{8}} = \frac{1}{15}\]

Probability of drawing a red marble from box B is given by P(E_B/R).

\[\therefore P\left( E_B /R \right) = \frac{P\left( E_B \cap R \right)}{P\left( R \right)} = \frac{\frac{6}{40}}{\frac{3}{8}} = \frac{2}{5}\]

Probability of drawing a red marble from box C is given by P(E_C/R)

\[\therefore P\left( E_C /R \right) = \frac{P\left( E_C \cap R \right)}{P\left( R \right)} = \frac{\frac{8}{40}}{\frac{3}{8}} = \frac{8}{15}\]