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?

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Solution

## Step $1$: Find the total number marbles in the boxNumber 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}}$$P\left(\mathrm{getting}\mathrm{red}\right)=\frac{5}{17}=0.29$$P\left(\mathrm{getting}\mathrm{white}\right)=\frac{8}{17}=0.47$$P\left(\mathrm{green}\right)=\frac{4}{17}=0.23$Step 3: Use the formula for the probability of complementary event$\because P\left(E\right)+P\left({E}^{\text{'}}\right)=1$$\therefore P\left(notgreen\right)=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 $0.77$

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