A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administration selects three students from the council at random. What is the chance that out of the selected students, two belong to the same school and the third belongs to different school?

Let $X$ be a continuous random variable defined on $[0, 1]$ such that its probability density function $f(x) = 1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y = \log_e (X + 1)$. Then the expected value of $Y$ is _____ . (rounded off to 2 decimal places)

Let a random variable X follow Poisson distribution such that

Prob(X = 1) = Prob(X = 2).

The value of Prob(X = 3) is __________ (round off to 2 decimal places).