The probability distribution of X is

X	0	1	2	3
P(X)	0.3	k	2k	2k

The value of k is

• 0.7

• 0.3

• 1

• 0.14

Two events A and B will be independent if

• $\mathrm{P}\left(\mathrm{A}\text{'} \cap \mathrm{B}\text{'}\right) = \left(1 - \mathrm{P}\left(\mathrm{A}\right)\right)\left(1 - \mathrm{P}\left(\mathrm{B}\right)\right)$

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) = 1$

• $\mathrm{P}\left(\mathrm{A}\right) = \mathrm{P}\left(\mathrm{B}\right)$

• A and B are mutually exclusive

There are four letters and four addressed envelopes. The chance that all letters are not despatched in the right envelope is

• 19/24

• 21/23

• 23/24

• None of these

224.

The mean and variance ofa random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is

• $\frac{1}{32}$

• $\frac{1}{16}$

• $\frac{1}{8}$

• $\frac{1}{4}$

If the mean and standard deviation in probability binomial distribution are 3 and 3/2 respectively, then the probability distribution is

• ${\left(\frac{3}{4} + \frac{1}{4}\right)}^{12}$

• ${\left(\frac{1}{4} + \frac{3}{4}\right)}^{12}$

• ${\left(\frac{1}{4} + \frac{3}{4}\right)}^9$

• ${\left(\frac{3}{4} + \frac{1}{4}\right)}^9$

A student appears in the test I, II, III. Student is declared pass if he passes any two of three tests. The probability of the student of pass test I, II, III are p, q and $\frac{1}{2}$. If the probability of student's success is $\frac{1}{2}$, then

• p = 1, q = 0

• $\mathrm{p} = \frac{2}{3}, \mathrm{q} = \frac{1}{2}$

• p, q have infinitly many values

• All of the above

If A and B are the events for which $\mathrm{P}\left(\mathrm{A}\right) = \frac{1}{3}, \mathrm{P}\left(\mathrm{B}\right) = \frac{1}{4} \mathrm{and} \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{5}$, then $\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)$ is equal to

• $\frac{4}{5}$

• $\frac{3}{5}$

• $\frac{7}{5}$

• $\frac{1}{5}$

The probability of a student of pass in Maths, Physics and Chemistry are m, p and c respectively. Probability of passing atleast in one subject is 75% and atleast in two subjects, is 50% and in exactly two subject is 40%, then which relation is correct ?

• $\mathrm{p} + \mathrm{m} + \mathrm{c} = \frac{19}{20}$

• $\mathrm{p} + \mathrm{m} + \mathrm{c} = \frac{27}{20}$

• $\mathrm{p} + \mathrm{m} + \mathrm{c} = \frac{1}{10}$

• None of these

A dice is rolled 6 times, if the appearance of an even number on it is assumed a success, then the probability of getting 5 success is

• $\frac{1}{32}$

• $\frac{3}{32}$

• $\frac{1}{16}$

• $\frac{5}{32}$

The probability that at least one ofthe events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then $\mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\overline{\mathrm{B}}\right)$ will be

• 1.5

• 1.3

• 1.2

• 0.8