# The odds against student X solving a statistics problem are 8:6 and odds in favour of student y solving the same problem are 14:16. Find is the chance that neither of them solves the problem - Mathematics and Statistics

Sum

The odds against student X solving a statistics problem are 8:6 and odds in favour of student y solving the same problem are 14:16. Find is the chance that neither of them solves the problem

#### Solution

The odds against X solving a problem are 8:6.

Let P(X') = P(X does not solve the problem)

= 8/(8 + 6)

= 8/14

So, the probability that X solves the problem

= P(X)

= 1 – P(X')

= 1 - 8/14

= 6/14

Similarly, let P(Y) = P(Y solves the problem) Since odds in favour of Y solving the problem are 14:16,

P(Y) = 14/(14 + 16)

= 14/30

So, the probability that Y does not solve the problem

= P(Y')

= 1 – P(Y)

= 1 - 14/30

= 16/30

Required probability = P(X' ∩ Y')

Since X and Y are independent events, X' and Y' are also independent events.

∴ Required probability = P(X').P(Y')

= 8/14 xx 16/30

= 32/105

Concept: Odds (Ratio of Two Complementary Probabilities)
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