Aspire Faculty ID #10316 · Topic: NIMCET 2013 · Just now
NIMCET 2013

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is

Solution

Let $P(\text{odd}) = 3k$ and $P(\text{even}) = k$. 
Since $P(\text{odd}) + P(\text{even}) = 1$: 
 $3k + k = 1$ 
 $4k = 1$ 
 $k = \frac{1}{4}$ 
So, $P(\text{odd}) = \frac{3}{4}$ $P(\text{even}) = \frac{1}{4}$ 
The sum of two numbers is even if: 
1. both are odd, or 
 2. both are even. 
 Therefore, $P(\text{even sum}) = P(\text{odd})^2 + P(\text{even})^2$ $= \left(\frac{3}{4}\right)^2 + \left(\frac{1}{4}\right)^2$ 
 $= \frac{9}{16} + \frac{1}{16}$ 
 $= \frac{10}{16}$ 
 $= \frac{5}{8}$ 
 So the probability that the sum is even is $\frac{5}{8}$.
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