List of top Mathematics & Statistics Questions on Probability

Defects on plywood sheet occur at random with the average of one defect per 50 sq.ft. Find the probability that such a sheet has : (a) no defect (b) at least one defect (use \(e^{-1} = 0.3678\))
Find the mean of number of heads in three tosses of a fair coin.
Five cards are drawn successively with replacement from a well shuffled deck of 52 cards. Find the probability that : (a) all the five cards are spades (b) only 3 cards are spades.
The expected value of the sum of two numbers obtained when two fair dice are rolled is ..............
If \( X \sim B(n, p) \) and \( E(X) = 6 \) and \( \text{Var}(X) = 4.2 \), then find \( n \) and \( p \).
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
Two dice are thrown simultaneously. If \( X \) denotes the number of sixes, find the expectation of \( X \).
If the p.m.f of a r.v. \( X \) is \( P(x) = \frac{c}{x^3} \), for \( x = 1, 2, 3 \), = 0 otherwise, then \( E(X) = \)