If P (A)=6/11,P (B)=5/11 and P (A ∪ B) = 7/11, find

i. P (A ∩ B)

ii. P (A /B)

iii. P (B/A)

State True or False for the statements in the Exercise.

If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then

Fill in the blanks in the following question:

If A and B are two events such that

and , then p = _____

A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?

Do you think that statement of B is true?

Often it is taken that a truthful person commands, more respect in the society. A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Do you also agree that the value of truthfulness leads to more respect in society?

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that

(i) the youngest is a girl?

(ii) atleast one is a girl?

A bag X contains 4 while balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.

OR

A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.