Probability (Class 12)

A bag contains 10 balls out of which k are red and (10 − k) are black, where 0 k 10. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:

1. 7110
2. 711
3. 755
4. 1455

The probability distribution of a random variable X is given below : array|c|c|c|c|c|c|c|c|c| X & 4k & 307k & 327k & 347k & 367k & 387k & 407k & 6k \ P(X) & 215 & 115 & 215 & 15 & 115 & 215 & 15 & 115 \ array If E(X) = 26315, then P(X < 20) is equal to :

1. 35
2. 1415
3. 815
4. 1115

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is

1. 73108
2. 67108
3. 7107
4. 81108

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is pq, (p, q) = 1, then p + q is equal to

1. 24
2. 22
3. 23
4. 21

If a random variable x has the probability distribution arrayccccccccc x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \ P(x) & 0 & 2k & k & 3k & 2k2 & 2k & k2 + k & 7k2 array then P(3 < x 6) is equal to

1. 0.34
2. 0.64
3. 0.22
4. 0.33

A random variable X takes values 0, 1, 2, 3 with probabilities 2a+130, 8a-130, 4a+130, b respectively, where a, b R. Let and respectively be the mean and standard deviation of X such that 2 + 2 = 2. Then ab is equal to:

1. 12
2. 60
3. 30
4. 3

If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P(A B) = 0.5, where B denotes the complement of B, then P (B (A B) ) is equal to

1. 13
2. 12
3. 14
4. 16

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is mn, (m, n) = 1, then n2 - m2 is equal to :

1. 64
2. 80
3. 60
4. 72

Let a random variable X take values 0, 1, 2, 3 with P(X = 0) = P(X = 1) = p, P(X = 2) = P(X = 3) and E(X2) = 2E(X). Then the value of 8p - 1 is :

1. 2
2. 0
3. 3
4. 1

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

1. 1115
2. 215
3. 35
4. 2875