Mathematics - Probability Question with Solution | TestHub

Let $P$ be the probability of getting an even number. Then by hypothesis the probability of getting an odd number is $3P$. Since the events of getting an even number and an odd number are mutually exclusive and exhaustive. $$\therefore P+3P=1\Rightarrow P=1/4$$ Thus, the probability of getting an odd number in a single throw is $\frac{3}{4}$ and that of an even number is $\frac{1}{4}$. If the die is thrown twice, then the sum of the numbers in two throws is even if both the numbers are even or both are odd. $$\therefore \text{ Required probability }=\frac{3}{4}\times \frac{3}{4}+\frac{1}{4}\times \frac{1}{4}=\frac{10}{16}=\frac{5}{8}$$