Advertisements
Advertisements
Question
If P (A|B) > P (A), then which of the following is correct:
Options
P(B|A) < P(B)
P(A ∩ B) < P(A) . P(B)
P(B|A) > P(B)
P(B|A) = P(B)
Solution
P(B|A) > P(B)
Explanation:
P(A|B) > P(A)
⇒ `(P(A ∩ B))/(P(B)) > P(A)`
∴ P(A ∩ B) > P(A) . P(B)
or `(P(A ∩ B))/(P(A)) > P(B)`
⇒ `P(B|A) > P(B)`
APPEARS IN
RELATED QUESTIONS
If A and B are events such that P (A|B) = P(B|A), then ______.
In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English news papers. A student is selected at random.
Find the probability that she reads neither Hindi nor English news papers.
In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English news papers. A student is selected at random.
If she reads Hindi news paper, find the probability that she reads English news paper.
In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English news papers. A student is selected at random.
If she reads English news paper, find the probability that she reads Hindi news paper.
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is ______.
Suppose that 5% of men and 0.25% of women have grey hair. A grey-haired person is selected at random. What is the probability of this person being male?
Assume that there are equal number of males and females.
An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:
P(A fails) = 0.2
P(B fails alone) = 0.15
P(A and B fail) = 0.15
Evaluate the following probabilities
- P(A fails| B has failed)
- P(A fails alone)
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
If A and B are two events such that P (A) ≠ 0 and P(B|A) = 1, then ______.
If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then ______.
A and B are two candidates seeking admission in a college. The probability that A is selected is 0.7 and the probability that exactly one of them is selected is 0.6. Find the probability that B is selected.
A committee of 4 students is selected at random from a group consisting 8 boys and 4 girls. Given that there is at least one girl on the committee, calculate the probability that there are exactly 2 girls on the committee.
A factory produces bulbs. The probability that anyone bulb is defective is `1/50` and they are packed in boxes of 10. From a single box, find the probability that none of the bulbs is defective
A factory produces bulbs. The probability that anyone bulb is defective is `1/50` and they are packed in boxes of 10. From a single box, find the probability that more than 8 bulbs work properly
A shopkeeper sells three types of flower seeds A1, A2 and A3. They are sold as a mixture where the proportions are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35%. Calculate the probability of a randomly chosen seed to germinate
A shopkeeper sells three types of flower seeds A1, A2 and A3. They are sold as a mixture where the proportions are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35%. Calculate the probability that it will not germinate given that the seed is of type A3
Three persons, A, B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is ______.
The probability of guessing correctly at least 8 out of 10 answers on a true-false type-examination is ______.
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is ______.
If A and B are such that P(A' ∪ B') = `2/3` and P(A ∪ B) = `5/9` then P(A') + P(B') = ______.
If 'A' and 'B' are events such that `P(A/B) = P(B/A)` then:-
Compute P(A/B) If P(B) = 0.5, P(A ∩ B) = 0.32
What will be the value of P(A ∪ B) it 2P(A) = P(B) = `5/13` and P(A/B) = `?/5`
If P(A) = `6/11`, P(B) = `5/11` and P(A ∪ B) = `7/11`, then what will be the value of P(A ∩ B)
Given that two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4.
Read the following passage and answer the questions given below.
 There are two antiaircraft guns, named as A and B. The probabilities that the shell fired from them hits an airplane are 0.3 and 0.2 respectively. Both of them fired one shell at an airplane at the same time. |
- What is the probability that the shell fired from exactly one of them hit the plane?
- If it is known that the shell fired from exactly one of them hit the plane, then what is the probability that it was fired from B?
A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on atleast one die.
