Probability Tes...

Let A and B be two events such that P(A) $$= \frac{3}{8}$$, P(B) $$= \frac{5}{8}$$ and P(A $$\cup$$ B) $$= \frac{3}{4}$$. Then $$P(A|B). P(A'|B)$$ is equal to

If two events are independent, then

A card is drawn from a well shuffled deck of 52 playing cards. The probability that the card drawn not an ace of diamond is E. Then number of favourable outcomes of E is:

Two events $$A$$ and $$B$$ are said to be mutually independent, if:

5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that there are exactly 3 hearts is

A bag contains 6 balls. Two balls are drawn and found to be red. The probability that five balls in the bag are red

A letter is known to have come form TATANAGAR or CALCUTTA. On the envelope just two consecutive letters TA are visible. The probability that the letter has come from CALCUTTA is

A bag contains 4 white and 5 black balls. A second bag contains 3 (identical) white and 6 (identical) black balls. One bag is chosen at random and a ball is drawn. Its colour is noted and the ball replaced. This is repeated four times. It was found that of these four, one was white and 3 were black. The $$n$$ the probability that the first bag was chosen is

5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that there are 4 hearts is

$$A$$ and $$B$$ are two independent witnesses in a case. The probability that $$A$$ will speak truth is $$x$$ and the probability that $$B$$ will speak the truth is $$y$$. $$A$$ and $$B$$ agree in a certain statement. The probability that the statement is true is