Advertisements
Advertisements
Question
Probability of solving specific problem independently by A and B are `1/2` and `1/3` respectively. If both try to solve the problem independently, find the probability that the problem is
- solved
- exactly one of them solves the problem
Solution
Given P(A) = `1/2` and P(B) = `1/3`
i. The probability that problem is solved = The probability that at least one solving the problem
= 1 – P(none of them solving the problem)
= `1 - "P"(bar"A" ∩ bar"B")`
= `1 - "P"(bar"A") xx "P"(bar"B")`
= `1 - (1 - 1/2) xx (1 - 1/3)`
= `1 - (1/2) xx (2/3)`
= `1 - 1/3`
= `2/3`
ii. P(exactly one of them solves the problem)
= `"P"(bar"A" ∩ "B") + "P"("A" ∩ bar"B")`
= `"P"(bar"A") xx "P"("B") + "P"("A") xx "P"(bar"B")`
= `(1 - 1/2)(1/3) + 1/2(1 - 1/3)`
= `1/2 xx 1/3 + 1/2 xx 2/3`
= `1/6 + 2/6`
= `3/6`
= `1/2`
APPEARS IN
RELATED QUESTIONS
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.
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?
From a pack of 52 cards, two cards are drawn at random. Find the probability that one is a king and the other is a queen.
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
If two events A and B are dependent then the conditional probability of P`("B"/"A")` is
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
- No woman
- One man
- No man
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) = 0.15, P(B) = 0.30, P(C) = 0.43, P(D)= 0.12
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
Choose the correct alternative:
There are three events A, B and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is
