JEE PYQ: Probability Question 23
Question 23 - 2020 (06 Sep Shift 1)
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:
(1) $\frac{15}{101}$
(2) $\frac{5}{101}$
(3) $\frac{5}{33}$
(4) $\frac{10}{99}$
Show Answer
Answer: (3)
Solution
For A.P., $2b = a + c$ (even), so $a$ and $c$ must be both even or both odd. Even numbers: 6, odd: 5 (or 5,6). ${}^6C_2 + {}^5C_2 = 15 + 10 = 25$. Required probability $= \frac{25}{{}^{11}C_3} = \frac{25}{165} = \frac{5}{33}$.
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