Question

# A die is tossed thrice. Find the probability of getting an odd number at least once.

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Solution

## We have,Number of possible outcomes on a die$=\left\{1,2,3,4,5,6\right\}$Favourable results getting even number$=\left(2,4,6\right)=3$Step 1: Calculate the probability of even number once$\begin{array}{rcl}\mathrm{Probability}\mathrm{of}\mathrm{getting}\mathrm{an}\mathrm{even}\mathrm{number}& =& \frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}\\ & =& \frac{3}{6}\\ & & \mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}3\\ & =& \frac{1}{2}\end{array}$Probability of getting even number once $=\frac{1}{2}$Step 2: Calculate the probability of even number thrice$\begin{array}{rcl}\mathrm{Probability}\mathrm{of}\mathrm{getting}\mathrm{even}\mathrm{number}\mathrm{thrice}& =& \frac{1}{2}×\frac{1}{2}×\frac{1}{2}\\ & =& \frac{1}{8}\end{array}$Step 3: Calculate the probability of getting at least one odd numberTherefore, probability of getting at least one odd number$\begin{array}{rcl}& =& 1-\frac{1}{8}\end{array}$ $=\frac{7}{8}$Hence, probability of getting an odd number at least once is $\frac{7}{8}$

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