Probability (Class 12)

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

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