If $\mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) = 0.8 \mathrm{and} \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = 0.3$, then $\mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\overline{\mathrm{B}}\right)$ is equal to :

• 0.3

• 0.5

• 0.8

• 0.9

A coin is tossed n times the probability of getting head at least once is greater than 0.8. Then, the least value of such n is :

• 2

• 3

• 4

• 5

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is

• ${\log }_{\mathrm{e}}\left(20\right)$

• ${\log }_{10}\left(20\right)$

• ${\log }_{\mathrm{e}}\left(\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)$

• 0

If the range of a random variable X is {0, 1, 2, 3, 4.....} with P(X = k) = $\frac{\left(\mathrm{k} + 1\right)\mathrm{a}}{3^{\mathrm{k}}}$, fork  > 0, then a is equal to

• $\frac{2}{3}$

• $\frac{4}{9}$

• $\frac{8}{27}$

• $\frac{16}{81}$

For a binomial variate X with n = 6, if P(X = 2) = 9 P(X = 4), then its variance is

• $\frac{8}{9}$

• $\frac{1}{4}$

• $\frac{9}{8}$

• 4

If A and B are two independent events such that

P(B) = $\frac{2}{7}, \mathrm{P}\left(\mathrm{A} \cup {\mathrm{B}}^{\mathrm{c}}\right)$= 0.8, then P(A) is equal to:

• 0.1

• 0.2

• 0.3

• 0.4

247.

A number n is chosen at random from {1, 2, 3, 4, . . . , 1000}. The probability that n is a number that leaves remainder 1 when divided by 7, is :

• $\frac{71}{500}$

• $\frac{143}{1000}$

• $\frac{72}{500}$

• $\frac{71}{1000}$

In the random experiment of tossing two unbiased dice let E be the event of getting the sum 8 and F be the event of getting even numbers on both the dice. Then :

I. P(E) = $\frac{7}{36}$ II. p (F) = $\frac{1}{3}$

Which of the following is a correct statement ?

• Both I and II are true

• Neither I nor II is true

• I is true, II is false

• I is false, II is true

The probability distribution of a random variable X is given by

The variance of X is

• 1.76

• 2.45

• 3.2

• 4.8

$$\begin{gathered} \mathrm{If} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{are} \mathrm{independent} \mathrm{events} \mathrm{of} \mathrm{arandom} \mathrm{experiment} \mathrm{such} \mathrm{that} \\ \mathrm{P}(\mathrm{A} \cap \mathrm{B}) = \frac{1}{6} \mathrm{and} \mathrm{P}\left(\overline{\mathrm{A}} \cap \overline{\mathrm{B}}\right) = \frac{1}{3}, \mathrm{then} \mathrm{P}\left(\mathrm{A}\right) = ? \end{gathered}$$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$