Question

A student has to match three historical events. Dandi March, Quit India movement and Mahatma Gandhi's assassination with years 1948, 1930 and 1942. The student has no knowledge of the correct answers and decides to match the events and years randomly. If $X$ denotes the number of correct answers he gets, then
$P(X=0)=.........$, $P(X=1)=.........$, $P(X=2)=........$ and $P(X=3)=........$

• A. $\frac{1}{6},\frac{1}{2},0,\frac{1}{3}$
• B. $\frac{1}{3},\frac{1}{6},0,\frac{1}{2}$
• C. $\frac{1}{2},\frac{1}{3},0,\frac{1}{6}$
• D. $\frac{1}{3},\frac{1}{2},0,\frac{1}{6}$

Answer 1

The correct option is D $\frac{1}{3},\frac{1}{2},0,\frac{1}{6}$

The number of ways in which the student can mark the answer is $\left(3\right)\left(2\right)\left(1\right)=6$.
All the three answer can be correct in just one way, eactly twoo correct is impossible, exactly one correct in $3$ ways and no correct in $2$ ways.
Therefore required probability are $\frac{1}{3},\frac{1}{2},0,\frac{1}{6}$