Advertisements
Advertisements
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.
Advertisements
उत्तर
Let A, E1, and E2 respectively denote the events that a person has a heart attack, the selected person followed the course of yoga and meditation, and the person adopted the drug prescription.
`therefore P(A)=0.40`
`P(E_1)=P(E_2)=1/2`
`P(A|E_1)=0.40xx0.70=0.28P(A|E_2)=0.40xx0.75=0.30`
Probability that the patient suffering a heart attack followed a course of meditation and yoga is given by `P (E1|A).`
`P(E_1|A)=(P(E_1)P(A|E_1))/(P(E_1)P(A|E_1)+P(E_2)P(A|E_2))`
`=(1/2xx0.28)/(1/2xx0.28+1/2xx0.30)`
`=14/29`
Let us calculate `P(E_2|A)`
`P(E_2|A)=(P(E_2)P(A|E_2))/(P(E_1)P(A|E_1)+P(E_2)P(A|E_2))`
`=(1/2xx0.30)/(1/2xx0.28+1/2xx0.30)`
`=15/29`
Since `P(E_1|A)< P(E_2|A) ` the course of yoga and meditation is more beneficial for a person having chances of heart attack.
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.
The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses
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)
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).
A die is thrown three times,
E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses
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 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.
In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.
Suppose we have four boxes. A, B, C and D containing coloured marbles as given below:
| Box | Marble colour | ||
| Red | White | Black | |
| A | 1 | 6 | 3 |
| B | 6 | 2 | 2 |
| C | 8 | 1 | 1 |
| D | 0 | 6 | 4 |
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?
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.
If events A and B are independent, such that `P(A)= 3/5`, `P(B)=2/3` 'find P(A ∪ B).
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
Two cards are drawn one after the other from a pack of 52 cards without replacement. What is the probability that both the cards drawn are face cards?
If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)
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?
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.
In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______
A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:
A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.
If P(A) = `1/2`, P(B) = 0, then `P(A/B)` is
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 ______.
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that at least two of them will solve the problem.
