Advertisements
Advertisements
प्रश्न
A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.
Find the probability of B, given that A has already occurred.
उत्तर
A is an event of getting 5 on the first throw and 6 on the second throw.
Then
A={(5,6,1) (5,6,2) (5,6,3) (5,6,4) (5,6,5) (5,6,6)}
Also, B is an event of getting 3 or 4 on the third throw.
∴ A∩B={(5,6,3), (5,6,4)}
Required probability, `P(A|B)=(n(A∩B))/(n(A))=2/6=1/3`
Thus, the probability of B, given that A has already occurred is 1/3
APPEARS IN
संबंधित प्रश्न
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls? Given that
- the youngest is a girl.
- at least one is a girl.
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.
A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.
Suppose that 80% of all families own a television set. If 5 families are interviewed at random, find the probability that
a. three families own a television set.
b. at least two families own a television set.
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)
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(A ∪ B)
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).
Mother, father and son line up at random for a family picture
E: son on one end, F: father in middle
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
A die is tossed thrice. Find the probability of getting an odd number at least once.
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.
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
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.
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
From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack
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 the problem is solved?
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 both are white
If X denotes the number of ones in five consecutive throws of a dice, then P(X = 4) is ______
Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.
Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.
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 ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
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 ______.
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.
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
