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).

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

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

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

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

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