Probability (Class 12)

There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag Y, is :

1. 12
2. 13
3. 512
4. 14

A company has two plants A and B to manufacture motorcycles. 60\% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80\% of the motorcycles manufactured at plant A are rated of the standard quality, while 90\% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is

1. 54
2. 66
3. 56
4. 64

From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of X is mn, where (m, n) = 1, then n - m is equal to .

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is 2, then 96 2 is equal to .

Let the mean and the standard deviation of the probability distribution [figure] be and , respectively. If - = 2, then + is equal to .

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is :

1. 417
2. 516
3. 518
4. 718

If the mean of the following probability distribution of a random variable X : [figure] is 469, then the variance of the distribution is

1. 58181
2. 56681
3. 15127
4. 17327

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