Advertisements
Advertisements
प्रश्न
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.
पर्याय
`2/9`
`7/9`
`4/9`
`5/9`
उत्तर
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to `underlinebb(2/9)`.
Explanation:
Given,
`P(A/B) = 2 xx P(B/A)`
`\implies (P(A ∩ B))/(P(B)) = 2 xx (P(A ∩ B))/(P(A))`
`\implies` P(A) = 2P(B) ...(i)
Now, P(A) + P(B) = `2/3`
From (i),
2P(B) + P(B) = `2/3`
`\implies` P(B) = `2/9`.
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
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.
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)
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
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).
Two coins are tossed once, where
E: no tail appears, F: no head appears
A black and a red dice are rolled.
Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)
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 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.
Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white ·and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up the box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball is drawn is white, what is the probability that the dice had turned up with a red face?
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?
If events A and B are independent, such that `P(A)= 3/5`, `P(B)=2/3` 'find P(A ∪ B).
A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?
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?
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
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, 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) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.
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:
If P(A) = `1/2`, P(B) = 0, then `P(A/B)` 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 ______.
Read the following passage:
|
Recent studies suggest the roughly 12% of the world population is left-handed.
Assuming that P(A) = P(B) = P(C) = P(D) = `1/4` and L denotes the event that child is left-handed. |
Based on the above information, answer the following questions:
- Find `P(L/C)` (1)
- Find `P(overlineL/A)` (1)
- (a) Find `P(A/L)` (2)
OR
(b) Find the probability that a randomly selected child is left-handed given that exactly one of the parents is left-handed. (2)
Students of under graduation submitted a case study on “Understanding the Probability of Left-Handedness in Children Based on Parental Handedness”. Following Recent studies suggest that roughly 12% of the world population is left-handed. Depending on the parents’ handedness, the chances of having a left-handed child are as follows:
Scenario A: Both parents are left-handed, with a 24% chance of the child being left-handed.
Scenario B: The fathers is right-handed and the mothers left-handed, with a 22% chance of child being left-handed.
Scenario C: The fathers left-handed and the mother is right-handed, with a 17% chance of child being left-handed.
Scenario D: Both parents are right-handed, with a 9% chance of having a left-handed child.
Assuming that scenarios A, B, C and D are equally likely and L denotes the event that the child is left-handed, answer the following questions.
- What is the overall probability that a randomly selected child is left-handed?
- Given that exactly one parent is left-handed, what is the probability that a randomly selected child is left-handed?
- If a child is left-handed, what is the probability that both parents are left-handed?
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
