M L Aggarwal Solutions for Chapter: Probability, Exercise 11: CHAPTER TEST

An insurance company insured $2000$scooter drivers, $4000$ car drivers and $6000$ truck drivers. The probabilities of accidents are $0.01, 0.03$ and $0.15$ respectively. One of the insured persons meets with an accident. If the probability that he is a scooter driver is $\frac{1}{k}$, then find the value of $k$.

Three bags contain balls as shown in the table below :

A bag is chosen at random and two balls are drawn from it. They happened to be white and red. What is the probability that they came from bag III?

Let X denote the number of colleges where you will apply after your results and P(X=x) denotes your probability of getting admission in x number of colleges. It is given that
$\left\{\begin{array}{c}\begin{array}{l}kx, if x=0 or 1\\ 2kx if x = 2\end{array}\\ k(5-x) if x=3 or 4\\ \end{array}\right.$
where k is a positive constant, find the value of k.

Let $X$ denote the number of colleges where you will apply after your results and $P(X=x)$ denotes your probability of getting admission in x number of colleges. It is given that
$\left\{\begin{array}{ll}kx& \mathrm{if} x=0 \mathrm{or} 1\\ 2kx& \mathrm{if} x=2\\ k(5-x)& \mathrm{if} x=3 \mathrm{or} 4\end{array}\right.$
Where $k$ is a constant
What is the probability that you will get admission in exactly two colleges?

The probability distribution of a discrete random variable X is given as under:

The probability distribution of a discrete random variable X is given as under:

A and B play a game in which A's chance of winning the game is $\frac{3}{5}$  . In a series of $6$ games, find the probability that A will win at least $4$ games.

If $20\%$ of the bolts produced by a machine are defective, determine the probability that out of $4$ bolts chosen at random less than $2$ bolts will be defective.