Question

A box contains $5$ red marbles, $8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

Answer 1

Step $1$: Find the total number marbles in the box

Number of red marbles in box $=5$

Number of white marbles in box $=8$

Number of green marbles in box$=4$

Total numbers of marbles in box$=5+8+4=17$
Step 2: Use the classical definition of probability
$\because P\left(E\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$

$P(\mathrm{getting}\mathrm{red})=\frac{5}{17}=0.29$

$P(\mathrm{getting}\mathrm{white})=\frac{8}{17}=0.47$

$P(\mathrm{green})=\frac{4}{17}=0.23$

Step 3: Use the formula for the probability of complementary event

$\because P\left(E\right)+P\left(E^{\text{'}}\right)=1$

$\therefore P(notgreen)=1-P\left(green\right)=1-\left(\frac{4}{7}\right)=0.77$

Hence, probability of getting red is $0.29$, probability of getting white is $0.47$ and probability of not getting green is $0.77$