JEE PYQ: Probability Question 9
Question 9 - 2021 (24 Feb Shift 2)
The probability that two randomly selected subsets of the set ${1, 2, 3, 4, 5}$ have exactly two elements in their intersection, is:
(1) $\frac{65}{2^8}$
(2) $\frac{135}{2^9}$
(3) $\frac{65}{2^7}$
(4) $\frac{35}{2^7}$
Show Answer
Answer: (2)
Solution
For each element, 4 possibilities: (in both, in A only, in B only, in neither). Total $= 4^5$. Elements in intersection: choose 2 from 5: ${}^5C_2 = 10$. Remaining 3 elements must not be in both: $3^3 = 27$ ways each. $P = \frac{10 \times 27}{4^5} = \frac{270}{1024} = \frac{135}{512} = \frac{135}{2^9}$.
BETA
