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Question

A dice is thrown 80 times. If the probability of having an even number is $$7/ 10$$ then how many times an odd number appears on dice?

Solution
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$${\textbf{Step -1: Finding the probability of getting an odd number}}$$

$${\text{Let the probability of having an odd number is P}}\left( {\overline E } \right) = x$$

$$\because {\text{P}}\left( E \right) + P\left( {\overline E } \right) = 1.$$

$$ \Rightarrow \dfrac{7}{{10}} + P\left( {\overline E } \right) = 1$$

$$ \Rightarrow P\left( {\overline E } \right) = 1 - \dfrac{7}{{10}}$$

$$ \Rightarrow P\left( {\overline E } \right) = \dfrac{{10 - 7}}{{10}} = \dfrac{3}{{10}}$$

$${\text{Hence, probability of having an odd number is }}\dfrac{3}{{10}}.$$

$${\textbf{Step -2: Finding how many times the odd number occurs when dice is thrown 80 times.}}$$

$$\because P\left( {\overline E } \right) = \dfrac{3}{{10}}$$

$$ \Rightarrow \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total outcomes}}}} = \dfrac{3}{{10}}$$

$$\left( {{\textbf{Using the formula: Probability = }}\dfrac{{{\textbf{Number of favorable outcomes}}}}{{{\textbf{Total outcomes}}}}} \right)$$

$$ \Rightarrow \dfrac{{{\text{Number of favourable outcomes}}}}{{80}} = \dfrac{3}{{10}}$$ $$\left( {\because {\textbf{Dice is thrown 80 times}}} \right)$$

$$ \Rightarrow {\text{Number of favourable outcomes}} = \dfrac{{3 \times 80}}{{10}} = 24$$

$${\text{Hence, 24 times odd number will occur when dice is thrown 80 times}}{\text{.}}$$

$${\textbf{Hence,24 times odd number will occur when dice is thrown 80 times.}}$$

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