Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. if one ball is now drawn from urn A, the probability that it is found to be red is

3 persons A,B,C are to speak at a function along with 5 other persons. If the persons speak in random order, the probability that A speaks before B and B speaks before C is

If the plane 2ax-3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x²+y²+z²+6x-8y-2z=13 and x²+y²+z²-10x+4y-2z=8 then a=

A is one of 6 horses entered for a race and is to be ridden by one of two jockeysP and Q. It is 2 to 1 that P rides A, in which case all the horses are likely to win. If Q rides A, his chance is tribled. The probability of A’s winning is

5 different engineering, 4 different mathematics and 2 different chemistry books are placed in a shelf at random. The probability that the books of each kind are all together is

In a class of 125 students 70 passed in Mathematics and 55 in statistics and 30 in both. The probability that a student, selected at random from the class, has passed in only one subject is

A man is known to speak the truth 2 out of 3 times. He throws a die and reports that it is a six. The probability that it is actually a five is

A bag contains 4 green, 6 black and 7 white balls. A ball is drawn at random .The probability that it is either black ball or a white ball is

The sum of the distances of any point on the ellipse 3x²+4y²=24 from its foci is

One ticket is selected at random from 100 tickets numbered 00,01,02,...99. Suppose A and B are the sum and product of the digits found on the ticket. Then P(A=7 | B=0) is given by