Probability

Suppose A and B are two events such that $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{3}{25} \mathrm{and} \mathrm{P}\left(\mathrm{B} - \mathrm{A}\right) = \frac{8}{25}. \mathrm{Then}, \mathrm{P}\left(\mathrm{B}\right)$ is equal to

• $\frac{11}{25}$

• $\frac{3}{11}$

• $\frac{1}{11}$

• $\frac{9}{11}$

Suppose that a random variable X follows Poisson distribution. If P(X = 1) = P(X = 2) then P(X = 5) is equal to

• $\frac{2}{3}{\mathrm{e}}^{- 2}$

• $\frac{3}{4}{\mathrm{e}}^{- 2}$

• $\frac{4}{15}{\mathrm{e}}^{- 2}$

• $\frac{7}{8}{\mathrm{e}}^{- 2}$

If the mean and variance of a binomial variable X are 2 and 1 respectively, then P(X $\ge$ 1) is equal to

• $\frac{2}{3}$

• $\frac{15}{16}$

• $\frac{7}{8}$

• $\frac{4}{5}$

Let A and B be events in a sample space S suchthat P(A) = 0.5, P(B) = 0.4 andP(A $\cup$ B) = 0.6. Observe the following lists

The correct match of List I from List II is

Two numbers are chosen at random from{1, 2, 3, 4, 5, 6, 7, 8} at a time. The probability that smaller of the two numbers is less than 4 is

• $\frac{7}{14}$

• $\frac{8}{14}$

• $\frac{9}{14}$

• $\frac{10}{14}$

Two fair dice are rolled. The probability of the sum of digits on their faces to be greater than or equal to 10 is

• $\frac{1}{5}$

• $\frac{1}{4}$

• $\frac{1}{8}$

• $\frac{1}{6}$

A bag contains 2n + 1 corns. It is known that n of these coins have a head on both sides, whereas the remaining n + 1 coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\frac{31}{42}$, then n is equal to

• 10

• 11

• 12

• 13

The random variable takes the values 1, 2, 3, 1 ..., m. If P(X = n) = $\frac{1}{\mathrm{m}}$ to each n, then the variance of X is

• $\frac{\left(\mathrm{m} + 1\right)\left(2\mathrm{m} + 1\right)}{6}$

• $\frac{{\mathrm{m}}^2 - 1}{12}$

• $\frac{\mathrm{m} + 1}{2}$

• $\frac{{\mathrm{m}}^2 + 1}{12}$

$\mathrm{If} \mathrm{X} \mathrm{is} \mathrm{a} \mathrm{poisson} \mathrm{variate} \mathrm{P}\left(\mathrm{X} = 1\right) = 2\mathrm{P}\left(\mathrm{X} = 2\right), \mathrm{then} \mathrm{P}\left(\mathrm{X} = 3\right) = ?$

• $\frac{{\mathrm{e}}^{ - 1}}{6}$

• $\frac{\mathrm{e}{ }^{ - 2}}{2}$

• $\frac{{\mathrm{e}}^{ - 1}}{2}$

• $\frac{{\mathrm{e}}^{ - 1}}{3}$

The probability distribution of a random variable is given below

Then P(0 ) < X < 5) =?

• $\frac{1}{10}$

• $\frac{3}{10}$

• $\frac{8}{10}$