Advertisements
Advertisements
प्रश्न
Solve the following:
Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("A"/"B")`
Advertisements
उत्तर
It is given that, P(A) = `1/4` and
P(A U B) = 2P(B) – P(A)
= `2"P"("B") - 1/4`
`"P"("A"/"B") ` = P(A) ...[∵ A, B are independent]
= `1/4`
APPEARS IN
संबंधित प्रश्न
A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.
A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white?
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
Let E and F be events with `P(E) = 3/5, P(F) = 3/10 and P(E ∩ F) = 1/5`. Are E and F independent?
Given that the events A and B are such that `P(A) = 1/2, PA∪B=3/5 and P (B) = p`. Find p if they are
- mutually exclusive
- independent.
If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and P(A ∩ B) = 1/8`, find P (not A and not B).
A speaks the truth in 60% of the cases, while B is 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?
If P(A) = 0·4, P(B) = p, P(A ⋃ B) = 0·6 and A and B are given to be independent events, find the value of 'p'.
The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that the couple will be alive 20 years hence.
The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that at least one of them will be alive 20 years hence.
The probability that a student X solves a problem in dynamics is `2/5` and the probability that student Y solves the same problem is `1/4`. What is the probability that
- the problem is not solved
- the problem is solved
- the problem is solved exactly by one of them
A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, the balls are of different color?
Bag A contains 3 red and 2 white balls and bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, and then a ball is drawn from that bag. Find the probability that both the balls drawn are of same color
A bag contains 3 red and 5 white balls. Two balls are drawn at random one after the other without replacement. Find the probability that both the balls are white.
Solution: Let,
A : First ball drawn is white
B : second ball drawn in white.
P(A) = `square/square`
After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining `square` balls.
∴ P(B/A) = `square/square`
∴ P(Both balls are white) = P(A ∩ B)
`= "P"(square) * "P"(square)`
`= square * square`
= `square`
A family has two children. Find the probability that both the children are girls, given that atleast one of them is a girl.
Solve the following:
If P(A ∩ B) = `1/2`, P(B ∩ C) = `1/3`, P(C ∩ A) = `1/6` then find P(A), P(B) and P(C), If A,B,C are independent events.
10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.
If A and B′ are independent events then P(A′ ∪ B) = 1 – ______.
A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A"/"B")`
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: P1P2
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: (1 – P1) P2
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: 1 – (1 – P1)(1 – P2)
Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x + y = 11} B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.
If A and B are independent events, then A′ and B′ are also independent
If A and B′ are independent events, then P(A' ∪ B) = 1 – P (A) P(B')
If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P(At least two of A, B, C occur) = 3p2 – 2p3
If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.
Let A and B be two events. If P(A | B) = P(A), then A is ______ of B.
Two events 'A' and 'B' are said to be independent if
Events A and Bare such that P(A) = `1/2`, P(B) = `7/12` and `P(barA ∪ barB) = 1/4`. Find whether the events A and B are independent or not.
The probability that A hits the target is `1/3` and the probability that B hits it, is `2/5`. If both try to hit the target independently, find the probability that the target is hit.
Five fair coins are tossed simultaneously. The probability of the events that at least one head comes up is ______.
Given two events A and B such that (A/B) = 0.25 and P(A ∩ B) = 0.12. The value P(A ∩ B') is ______.
