A point - - - - - is selected at random from inside of triangle formed by x-y-10 and both the co-ordinate axes- If - - are odd integers- then the probability that both - - are prime numbers- is

For (0,0), 0+0 10 lt;0 For point (α,β) to be inside the triangle, nbsp;α + β lt;10 If α, β are odd integers, possible points are (1,1), (1,3), nbsp;(1 ...

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Quantitative Aptitude

Probability

A point α, β ...

Question

A point $(α, β),$ $α, β \in Z$ is selected at random from inside of triangle formed by $x + y = 10$ and both the co-ordinate axes. If $α, β$ are odd integers, then the probability that both $α, β$ are prime numbers, is

\frac{1}{12}

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\frac{3}{10}

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\frac{5}{18}

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\frac{1}{3}

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Solution

The correct option is B $\frac{3}{10}$
For $(0, 0), 0 + 0 - 10 < 0$
For point $(α, β)$ to be inside the triangle,
$α + β < 10$
If $α, β$ are odd integers, possible points are
$(1, 1), (1, 3), (1, 5), (1, 7), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (7, 1)$
Total cases $= 10$
If $α, β$ are primes, possible points are
$(3, 3), (3, 5), (5, 3)$
Total such cases $= 3$

$∴$ Required probability $= \frac{3}{10}$

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A point (α,β), α,β∈Z is selected at random from inside of triangle formed by x+y=10 and both the co-ordinate axes. If α,β are odd integers, then the probability that both α,β are prime numbers, is

A point $(α, β),$ $α, β \in Z$ is selected at random from inside of triangle formed by $x + y = 10$ and both the co-ordinate axes. If $α, β$ are odd integers, then the probability that both $α, β$ are prime numbers, is