The odds against solving a problem by A and B are 3 : 2 and 2 : 1 respectively, then the probability that the problem will be solved, is

• $\frac{3}{5}$

• $\frac{2}{15}$

• $\frac{2}{5}$

• $\frac{11}{15}$

If random variable waiting time in minutes for bus and probability density function of x is given by

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right) = \left\{\frac{1}{5}, 0 \le \mathrm{x} \le 5 \\ 0 , \mathrm{otherwise}\right\} \end{gathered}$$

then probability of waiting time not more than 4 minutes is equal to

• 0.3

• 0.8

• 0.2

• 0.5

If the probability density function of a random variable X is given as

xi	- 2	- 1	0	1	2
P(X = xi)	0.2	0.3	0.15	0.25	0.1

then F(0) is equal to

• P(X < 0)

• P(X > 0)

• 1 - P(X > 0)

• 1 - P(X < 0)

If random variable $\mathrm{X} ~ \mathrm{B}\left(\mathrm{n} = 5, \mathrm{P} = \frac{1}{3}\right)$, then P(2 < X < 4) is equal to

• $\frac{80}{243}$

• $\frac{40}{243}$

• $\frac{40}{343}$

• $\frac{80}{343}$

At random variable X $~$ B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are

• 54

• 55

• 12

• 18

Probability that a person will develop immunity after vaccinations is 0.8. If 8 people are given the vaccine, then probability that all develop immunity is =

• (0.2)⁸

• (0.8)⁸

• 1

• ${}^8\mathrm{C}_6{\left(0.2\right)}^6{\left(0.8\right)}^2$

For the following distribution function F(x) of a rv.X.

x	1	2	3	4	5	6
F(x)	0.2	0.37	0.48	0.62	0.85	1

$\mathrm{P}\left(3 < \mathrm{x} \le 5\right)$ =

• 0.48

• 0.37

• 0.27

• 1.47

Probability of solving a particular question by person A is 1/3 and probability ofsolving that question by person B is 2/5. what is the probability of solving that question by atleast one of them ?

• $\frac{3}{5}$

• $\frac{7}{9}$

• $\frac{2}{5}$

• $\frac{2}{3}$

The probabilities that Mr. A and Mr. B will die within a year are $\frac{1}{2} \mathrm{and} \frac{1}{3}$ respectively, then the probability that only one of them will be alive at the end of the year, is

• $\frac{5}{6}$

• $\frac{1}{2}$

• $\frac{2}{3}$

• None of the above

1200.

The probability that a man will live 10 more years, is $\frac{1}{4}$ and the probability that his wife  will live 10 more years, is $\frac{1}{3}$. Then, what is the probability that neither will be alive in 10 yr ?

• $\frac{1}{2}$

• $\frac{3}{7}$

• $\frac{2}{3}$

• $\frac{1}{4}$