Probability (Class 12)

In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 13 and 23 respectively. Let x be the number of matches that the team wins, and y be the number of matches that team loses. If the probability P(|x - y| 2) is p, then 39 p equals .

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is :

1. 25
2. 27
3. 17
4. 15

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

1. 57153
2. 40153
3. 37153
4. 47153

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

1. 425
2. 23
3. 225
4. 475

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

1. 19
2. 29
3. 127
4. 227

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

1. 1/4
2. 1/3
3. 3/10
4. 1/9

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

1. 511
2. 56
3. 16
4. 611

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a=P(X=3), b=P(X 3) and c=P(X 6 X>3). Then b+ca is equal to .

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

1. 3256
2. 5256
3. 3715
4. 5715