Advertisements
Advertisements
Question
If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A/B) and P(A ∪ B)
Advertisements
Solution
Given P(A) = 0.5
P(B) = 0.8
and P(B/A) = 0.8
P(A/B) = `("P"("A" ∩ "B"))/("P"("B"))` .........(1)
P(B/A) = `("P"("B" ∩ "A"))/("P"("A"))`
P(A ∩ B) = P(B/A) P(A)
Substituting in equation (1) we get
(1) ⇒ P(A/B) = `("P"("B"/"A") * "p"("A"))/("P"("B"))`
= `(0.8 xx 0.5)/0.8`
P(A/B) = 0.5
P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .........(2)
We have P(A/B) = `("P"("A" ∩ "B"))/("P"("B"))`
P(A ∩ B) = P(A/B) . P(B)
= 0.5 × 0.8
P(A ∩ B) = 0.40
(2) ⇒ P(A ∪ B) = 0.5 + 0.8 – 0.40
= 1.3 – 0.40
P(A ∪ B) = 0.90
APPEARS IN
RELATED QUESTIONS
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.
40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostelers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hosteler ?
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.
Determine P(E|F).
Two coins are tossed once, where
E: tail appears on one coin, F: one coin shows head
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.
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, one is white and other is black?
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 black
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) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.
If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.
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.
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is ______.
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to ______.
If A and B are events and \[P(B) \neq 0\], which expression gives \[P(A \mid B)\]?
Which statement is the multiplication rule for two events A and B?
Which complement form is correct when \[P(B)\neq 0\]?
Which conditional probabilities are equal to 1 when \[P(F)\neq 0\]?
Which sequence correctly applies a given condition when finding a conditional probability?
