A coin and six faced die, both unbiassed, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

• $\frac{1}{2}$

• $\frac{3}{4}$

• $\frac{1}{4}$

• $\frac{2}{3}$

A number n is chosen at random from S = {1, 2, 3, ... , 50}. LetA = {n ∈ S:n + 50/n > 27}, B={n ∈ S : n is a prime) and C = {n ∈ S : n is a square). Then,correct order of their probabilities is

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

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

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

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

Box A contains 2 black and 3 red balls, while Box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing Box A is double that of Box B. If a red ball is drawn from the selected box, then the probability that it has come from Box B

• $\frac{21}{41}$

• $\frac{10}{31}$

• $\frac{12}{31}$

• $\frac{13}{41}$

Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is :

• $\frac{7}{{}^{11}\mathrm{C}_7}$

• $\frac{{}^5\mathrm{C}_3 + {}^6\mathrm{C}_4}{{}^{11}\mathrm{C}_7}$

• $\frac{{}^5\mathrm{C}_2 {}^6\mathrm{C}_2}{{}^{11}\mathrm{C}_7}$

• $\frac{{}^6\mathrm{C}_3 {}^5\mathrm{C}_4}{{}^{11}\mathrm{C}_7}$

In a book of 500 pages, it is found that there are 250 typing errors. Assume that Poisson law holds for the number of errors per page. Then,the probability that a random sample of 2 pages will contain no error, is :

• e ^{- 3}

• e ^{- 5}

• e ^{- 1}

• e ^{- 2}

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.$

89.

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

• $\frac{14}{40}$

• $\frac{15}{40}$

• $\frac{16}{40}$

• $\frac{17}{40}$