Mathematics : Probability

Four numbers are chosen at random from{1, 2, 3, ..., 40}. The probability that they are not consecutive, is

• $\frac{1}{2470}$

• $\frac{4}{7969}$

• $\frac{2469}{2470}$

• $\frac{7965}{7969}$

If A and B are mutually exclusive events with P(B) $\ne$ 1, then P(A$|$$\overline{\mathrm{B}}$) is equal to(Here is the complement of the event B)

• $\frac{1}{\mathrm{P}\left(\mathrm{B}\right)}$

• $\frac{1}{1 - \mathrm{P}\left(\mathrm{B}\right)}$

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

• $\frac{\mathrm{P}\left(\mathrm{A}\right)}{1 - \mathrm{P}\left(\mathrm{B}\right)}$

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$15$}\right.$

• $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$

• $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$15$}\right.$

• $\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$15$}\right.$

The probability of choosing randomly a numberc from the set {1, 2, 3, . . . , 9} such that the quadratic equation  x² + 4x + c = 0 has real roots is

• $\frac{1}{9}$

• $\frac{2}{9}$

• $\frac{3}{9}$

• $\frac{4}{9}$

An urn A contains 3 white and 5 black balls. Another um B contains 6 white and 8 black balls. A ball is picked from A at random andthen transferred to B. Then, a ball is picked at random from B. The probability that it is a white ball is

• $\frac{14}{40}$

• $\frac{15}{40}$

• $\frac{16}{40}$

• $\frac{17}{40}$

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

• $\frac{1}{2}$

• $\frac{7}{15}$

• $\frac{2}{15}$

• $\frac{1}{3}$

The probability distribution of a random variable X is given below

X = x	0	1	2	3
P(X) = x	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

Then the variance of X is

• 1

• 2

• 3

• 4

The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is

• $\frac{1}{{\mathrm{e}}^2}$

• $\frac{2}{3{\mathrm{e}}^2}$

• $\frac{8}{3{\mathrm{e}}^2}$

• $\frac{4}{3{\mathrm{e}}^2}$

A regular polygon of n sides has 170 diagonals,then n is equal to

• 12

• 17

• 20

• 25

A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is

• 2720

• 2702

• 2270

• 2278