Probability (Class 12)

A coin is tossed three times. Let X denote the number of times a tail follows a head. If and 2 denote the mean and variance of X, then the value of 64 ( + 2 ) is:

1. 64
2. 32
3. 51
4. 48

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is mn, where (m,n)=1, then m+n is equal to :

1. 4
2. 14
3. 11
4. 13

If A and B are two events such that P(A B)=0.1, and P(A B) and P(B A) are the roots of the equation 12x2-7x+1=0, then the value of P( A B)P( A B) is :

1. 43
2. 74
3. 94
4. 53

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and yellow balls. If X and Y are the means of X and Y respectively, then 7 X + 4 Y is equal to .

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