A random variate X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2P(X = 1) and P(X = 2) = 0.3, then P(X = 0) is equal to :

• 0.1

• 0.2

• 0.3

• 0.4

692.

An unbiased coin is tossed to get 2 points forturning up a head and one point for the tail.If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{8}$

• $\frac{3}{8}$

Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given E is 1/10, then the probability of non-occurrence of atleast one of the events E and F is

• $\frac{1}{18}$

• $\frac{1}{2}$

• $\frac{49}{50}$

• $\frac{1}{50}$

Six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the upper most faces of the dice is an odd number is

• $\frac{5}{18}$

• $\frac{5}{36}$

• $\frac{13}{18}$

• $\frac{25}{36}$

A person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score X is observed, then the range of x is

• {0, 3, 6}

• {- 3, 0, 3}

• {- 3, 0, 3, 6}

• {- 3, 3, 6}

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}