Amit M Agarwal Solutions for Chapter: Advanced Probability, Exercise 4: Target Exercises

A pair of dice is rolled together till a sum of either $5$ or $7$ is obtained. The probability that $5$ comes before $7$, is

Let $F$ denotes the set of all onto functions from $A=\left\{a_1,a_2,a_3,a_4\right\}$  to $B=\left\{x,y,z\right\}$, A function $f$ is chosen at random from $F$. The probability that $f^{-1}\left(x\right)$ consists of exactly two elements, is

The value of $m$ for Poisson's distribution is

The mean of Poisson's distribution with parameter $m$ is

In Poisson's distribution, $P\left(x\right)$ for $x=0$ is $10\%$. The mean of distribution is

For a Poisson variate $x, P\left(x=2\right)=3 P\left(x=3\right)$, then mean is

Assuming distribution to be Poisson, the probability that atmost $5$ defective bolts will be found in a box of $200$ bolts, if it is known that $2\%$ of such bolts are defective, is

In a precision bombing attack, there is a $50\%$ chance that any one bomb will strike the target. Two direct hits are required to destroy the target completely. The number of bombs which should be dropped to give a $99\%$ chance or better of completely destroying the target, can be