Advertisements
Advertisements
Question
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Advertisements
Solution
Given P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2
`P(E|F) = (P(E ∩ F))/(P(E)) = 0.2/0.3 = 2/3`
and `P(F|E) = (P(E ∩ F))/(P(E)) = 0.2/0.6 = 1/3`
APPEARS IN
RELATED QUESTIONS
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
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.
Determine P(E|F).
A coin is tossed three times, where
E: head on third toss, F: heads on first two tosses
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)
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A is a subset of B.
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.
If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball is drawn is black.
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.
Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one by one without replacement. What is the probability that at least one ball is red?
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?
In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.
From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when first card drawn is kept aside
A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that exactly one of them will solve it?
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?
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that one white and one black
Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive
A year is selected at random. What is the probability that it contains 53 Sundays
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?
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 ∩ B) = `7/10` and P(B) = `17/20`, then P(A|B) equals ______.
Two cards are drawn out randomly from a pack of 52 cards one after the other, without replacement. The probability of first card being a king and second card not being a king is:
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 ______.
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 ______.
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 ______.
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?
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
If P(B) = `3/5`, P(A | B) = `1/2` and P(A ∪ B) = `4/5`, then P(A ∪ B) + P(A' ∪ B) =
For a two-child family, let E be “both children are boys” and F be “at least one child is a boy.” Which pair correctly gives E and F?
If A and B are any two events of S and \[P(F)\neq 0\], which formula is correct?
