Advertisements
Advertisements
प्रश्न
If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.
पर्याय
`5/6`
`5/7`
`25/42`
1
Advertisements
उत्तर
If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to `25/42`.
Explanation:
Given that: P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`
P(A') = `1 - 2/5 = 3/5`
P(B') = `1 - 3/10 = 7/10`
And P(A' ∩ B') = 1 – P(A ∪ B)
= 1 – [P(A) + P(B) – P(A ∩ B)]
= `1 - [2/5 + 3/10 - 1/5]`
= `1 - [1/5 + 3/10]`
= `1 - 5/10`
= `1/2`
∴ `"P"("A'"/"B'") = ("P"("A'" ∩ "B'"))/("P"("B'"))`
= `(1/2)/(7/10)`
= `5/7`
And `"P"("B'"/"A'") = ("P"("A'" ∩ "B'"))/("P"("A'"))`
= `(1/2)/(3/5)`
= `5/6`
∴ `"P"("A'"/"B'")*"P"("B'"/"A'") = 5/7 xx 5/6`
= `25/42`
APPEARS IN
संबंधित प्रश्न
The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses
Determine P(E|F).
A coin is tossed three times, where
E: head on third toss, F: heads on first two tosses
Determine P(E|F).
A coin is tossed three times, where
E: at most two tails, F: at least one tail
Determine P(E|F).
A die is thrown three times,
E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses
A black and a red dice are rolled.
Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)
Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
If A and B are events such as that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`, then find
1) P(A / B)
2) P(B / A)
A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both?
Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.
Three cards are drawn at random (without replacement) from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of red cards. Hence, find the mean of the distribution.
A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
Can two events be mutually exclusive and independent simultaneously?
If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent
If for two events A and B, P(A) = `3/4`, P(B) = `2/5` and A ∪ B = S (sample space), find the conditional probability P(A/B)
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(A/B) = 0.4
A year is selected at random. What is the probability that it contains 53 Sundays
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
If P(A) = `4/5`, and P(A ∩ B) = `7/10`, then P(B|A) is equal to ______.
If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.
If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:
A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.
If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to ______.
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is ______.
For a biased dice, the probability for the different faces to turn up are
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| P | 0.10 | 0.32 | 0.21 | 0.15 | 0.05 | 0.17 |
The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.
Let A, B be two events such that the probability of A is `3/10` and conditional probability of A given B is `1/2`. The probability that exactly one of the events A or B happen equals.
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.
If for any two events A and B, P(A) = `4/5` and P(A ∩ B) = `7/10`, then `P(B/A)` is equal to ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that at least two of them will solve the problem.
If P(B) = `3/5`, P(A | B) = `1/2` and P(A ∪ B) = `4/5`, then P(A ∪ B) + P(A' ∪ B) =
