Advertisements
Advertisements
प्रश्न
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(A/B) = 0.4
Advertisements
उत्तर
P(A) = 0.4
P(A ∪ B) = 0.7
P(A/B) = 0.4
(i.e.,) `("P"("A" ∩ "B"))/("P"("B"))` = 0.4
⇒ P(A ∩ B) = 0.4 [P(B)] ...........(i)
But we know P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
P(A ∩ B) = P(A) + P(B) – P(A ∪ B)
⇒ P(A ∩ B) = 0.4 + P(B) – 0.7
= P(B) – 0.3 .........(ii)
From (i) and (ii) (Equating R.H.S) we get
0.4 [P(B)] = P(B) – 0.3
0.3 = P(B)(1 – 0.4)
0.6 (P(B)) = 0.3
⇒ P(B) = `0.3/06`
= `3/6`
= 0.5
APPEARS IN
संबंधित प्रश्न
Assume that the chances of a patient having a heart attack is 40%. Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga. Interpret the result and state which of the above stated methods is more beneficial for the patient.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find
- P(A ∩ B)
- P(A|B)
- P(A ∪ B)
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
Determine P(E|F).
Two coins are tossed once, where
E: tail appears on one coin, F: one coin shows head
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
Determine P(E|F).
Mother, father and son line up at random for a family picture
E: son on one end, F: father in middle
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’.
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
Bag A contains 4 white balls and 3 black balls. While Bag B contains 3 white balls and 5 black balls. Two balls are drawn from Bag A and placed in Bag B. Then, what is the probability of drawing a white ball from Bag B?
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?
The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
It is given that the events A and B are such that P(A) = `1/4, P(A/B) = 1/2` and `P(B/A) = 2/3`, then P(B) is equal to ______.
Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result.
- What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
- What is the probability that they will get a different result in one round of tossing?
- What is the probability that they will need exactly four rounds of tossing to determine who would pay?
