A bag contains 5 white and 3 black balls and 4 balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is :

• 1/196

• 2/7

• 1/7

• 13/56

A class has 175 students. The following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone ?

• 35

• 48

• 60

• 22

If birth to a male child and birth to a female child are equal-probable, then what is the probability that at least one of the three children born to a couple is male ?

• $\frac{4}{5}$

• $\frac{7}{8}$

• $\frac{8}{7}$

• $\frac{1}{2}$

Two persons A and B throw a die alternately till one of them gets a 3 and wins the game, the respective probabilities of winning, if A begins, are :

• $\frac{7}{11}, \frac{4}{11}$

• $\frac{6}{11}, \frac{5}{11}$

• $\frac{5}{6}, \frac{1}{6}$

• $\frac{4}{7}, \frac{3}{7}$

185.

If three natural numbers from 1 to 100 are selected randomly, then probability that all are divisible by both 2 and 3, is :

• $\frac{4}{105}$

• $\frac{4}{33}$

• $\frac{4}{35}$

• $\frac{4}{1155}$

A bag contains 3 black, 3 white and 2 red balls. One by one, three balls are drawn without replacement. The probabilitythat the third ball is red is equal to :

• $\frac{2}{56}$

• $\frac{3}{56}$

• $\frac{1}{56}$

• $\frac{14}{56}$

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :

• $\frac{1}{17}$

• $\frac{1}{10}$

• $\frac{1}{11}$

• $\frac{1}{12}$

Unbiased die is thrown, probability that outcome is greater than 4, is

• 3/4

• 4/5

• 1/3

• 5/6

Probability P(A) = 0. 7, P(B) = 0.4, P(A $\cap$ B) = 0.3, then P(A $\cap$ B') is equal to

• 0.1

• 0.3

• 0.2

• 0.4

Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is 

• $\frac{10}{21}$

• $\frac{11}{13}$

• $\frac{13}{25}$

• $\frac{21}{32}$