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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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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