Advertisements
Advertisements
Question
An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
P(A) = `2/5`, P(B) = `3/5`, P(C) = `- 1/5`, P(D) = `1/5`
Solution
When A, B, C, D are the possible exclusive and exhaustive events the P(A) + P(B) + P(C) + P(D) = 1.
P(A) = `2/5`, P(B) = `3/5`, P(C) = `- 1/5`, P(D) = `1/5`
P(C) = `- 1/5` which is not possible
(i.e.) for any event A, (0 ≤ P(A) ≤ 1)
∴ The assignment of probability is not permissible.
APPEARS IN
RELATED QUESTIONS
A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?
An unbiased die is thrown twice. Let the event A be the odd number on the first throw and B the event odd number on the second throw. Check whether A and B events are independent.
Suppose one person is selected at random from a group of 100 persons are given in the following
| Title | Psychologist | Socialist | Democrat | Total |
| Men | 15 | 25 | 10 | 50 |
| Women | 20 | 15 | 15 | 50 |
| Total | 35 | 40 | 25 | 100 |
What is the probability that the man selected is a Psychologist?
Two urns contain the set of balls as given in the following table
| Title | White | Red | Black |
| Urn 1 | 10 | 6 | 9 |
| Urn 2 | 3 | 7 | 15 |
One ball is drawn from each urn and find the probability that
- both balls are red
- both balls are of the same colour.
The first of three urns contains 7 White and 10 Black balls, the second contains 5 White and 12 Black balls and the third contains 17 White balls and no Black ball. A person chooses an urn at random and draws a ball from it. And the ball is found to be White. Find the probabilities that the ball comes from
- the first urn
- the second urn
- the third urn
Three horses A, B, C are in the race. A is twice as likely to win as B and B is twice as likely to win as C. What are their respective probabilities of winning?
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 4. What is the probability that it is an even number?
There are 1000 students in a school out of which 450 are girls. It is known that out of 450, 20% of the girls studying in class XI. A student is randomly selected from 1000 students. What is the probability that the selected student is from class XI given that the selected student is a girl?
A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of drawing
- two aces
- two spades
The two events A and B are mutually exclusive if
If two events A and B are dependent then the conditional probability of P`("B"/"A")` is
Probability of an impossible event is _________.
Probability that at least one of the events A, B occur is
Eight coins are tossed once, find the probability of getting exactly two tails
A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that all are red
A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?
Suppose P(B) = `2/5`. Express the odds event B occurs
Choose the correct alternative:
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be
