Four numbers are chosen at random from{1, 2, 3, ..., 40}. The probability that they are not consecutive, is
If A and B are mutually exclusive events with P(B) 1, then P(A) is equal to(Here is the complement of the event B)
A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is
The probability of choosing randomly a numberc from the set {1, 2, 3, . . . , 9} such that the quadratic equation x2 + 4x + c = 0 has real roots is
An urn A contains 3 white and 5 black balls. Another um B contains 6 white and 8 black balls. A ball is picked from A at random andthen transferred to B. Then, a ball is picked at random from B. The probability that it is a white ball is
D.
Case Ist: Let a white ball be transfered from the first bag to the second bag.
The probability of selecting white ball from the first bag is
P1 =
Now, the second bag has 7 white and 8 black balls. The probability of selecting a white ballfrom the second bag is
P2 =
The probability that both these events take place simultaneously
Case IInd: Let a black ball be transfered fromthe first bag to the second bag. Its probability is
Now, the second 9 black balls.bag contains 6 white and
The probability of drawing a white ball from the second bag is P4 =
Therefore, the probability of both these events taking place simultaneously
=
Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is
The probability distribution of a random variable X is given below
X = x | 0 | 1 | 2 | 3 |
P(X) = x |
Then the variance of X is
1
2
3
4
The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is
A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is
2720
2702
2270
2278