The odds against A solving a problem are 8 to 6 and the odds in favour of B solving the same problem are 14 to 10. Then the probability that the problem will be solved if both of them try the problem is

Three numbers are selected at random without replacement from the set of numbers {1,2,...,n}. The conditional probability that the third number lies between the first two, if the first number is known to be smaller than the second, is

A bag consists a white and b black balls. Two players A and B alternatively draw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, then a:b=

There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that at least one letter may be placed in wrongly addressed envelope is

India plays two matches each with west indies and Australia. In any match the probabilities of India getting points 0,1 and 2 are 0.45,0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of getting at least 7points is

A student appears for test I,II and III. The student is successful if he passes either in tests I and II or III. The students passing in tests I,II and III are p, q and 1/2respectively.Ifthe probability that the student is successful is 1/2 then

3 faces of a fair die are yellow, two faces red and one blue. The die is tossed 3 times. The probability that the colours yellow, red and blue appear in the second and third tosses respectively is

100 tickets are numbered as 00,01, 02,...,09,10,11,...99. When a ticket is drawn at random from them and if B is the event of getting 0 as the product of the numbers on the ticket, then P(B)=

I. In a class 25% of thestudents failed in mathematics, 30% failed in chemistry and 15% failed in both Mathematics and chemistry. If a student is selected at random failed in Mathematics, the probability that he failed in chemistry is 1/2

II: A bag contain 10 identical balls of which 4 are blue and 6 are red. 3 balls are taken out at random from the bag one after the other. The probability that all the 3 balls drawn are red is 1/6

If 2 numbers are randomly selected from 20 consecutive natural numbers, then the probability that the sum of the two numbers is an even number is