If $P$ and $Q$ each toss three coins,the probability that both get the same number of heads is

If an unbiased die,marked with $-2, -1, 0, 1, 2, 3$ on its faces,is thrown five times,then the probability that the product of the outcomes is positive is:

Consider $5$ independent Bernoulli trials,each with a probability of success $p$. If the probability of at least one failure is greater than or equal to $31/32$,then in which interval does $p$ lie?

In order to get a head at least once with probability $\geq 0.9$, the minimum number of times an unbiased coin needs to be tossed is

$A$ die is rolled $5$ times. Getting an odd number in one trial is considered as a success. The variance of the distribution of successes is

$X$ denotes the number of times heads occur in $n$ tosses of a fair coin. If $P(X=4)$,$P(X=5)$,and $P(X=6)$ are in arithmetic progression,the largest value of $n$ is