Advertisements
Advertisements
Question
Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals ______.
Options
`2/7`
`3/35`
`1/70`
`1/7`
Advertisements
Solution
Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals `1/70`.
Explanation:
Given that: E and F are independent events such that
P(E) = 0.3 and P(E ∪ F) = 0.5
P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
0.5 = 0.3 + P(F) – P(E).P(F)
⇒ 0.5 – 0.3 = P(F)[1 – P(E)]
⇒ 0.2 = P(F)(1 – 0.3)
⇒ 0.2 = P(F).(0.7)
∴ P(F) = `0.2/0.7 = 2/7`
Now `"P"("E"/"F") - "P"("F"/"E") = ("P"("E" ∩ "F"))/("P"("F")) - ("P"("E" ∩ "F"))/("P"("E"))`
= `("P"("E")."P"("F"))/("P"("F")) - ("P"("E")."P"("F"))/("P"("E"))`
= P(E) – P(F)
= `3/10 - 2/7`
= `1/70`
APPEARS IN
RELATED QUESTIONS
If A and B are two independent events such that `P(barA∩ B) =2/15 and P(A ∩ barB) = 1/6`, then find P(A) and P(B).
If `P(A) = 3/5 and P(B) = 1/5` , find P (A ∩ B) if A and B are independent events.
If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and P(A ∩ B) = 1/8`, find P (not A and not B).
One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?
E : ‘the card drawn is a king or queen’
F : ‘the card drawn is a queen or jack’
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability `1/2`).
A speaks the truth in 60% of the cases, while B is 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?
If P(A) = 0·4, P(B) = p, P(A ⋃ B) = 0·6 and A and B are given to be independent events, find the value of 'p'.
A fair die is rolled. If face 1 turns up, a ball is drawn from Bag A. If face 2 or 3 turns up, a ball is drawn from Bag B. If face 4 or 5 or 6 turns up, a ball is drawn from Bag C. Bag A contains 3 red and 2 white balls, Bag B contains 3 red and 4 white balls and Bag C contains 4 red and 5 white balls. The die is rolled, a Bag is picked up and a ball is drawn. If the drawn ball is red; what is the probability that it is drawn from Bag B?
A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, exactly two students solve the problem?
The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that at least one of them will be alive 20 years hence.
The probability that a student X solves a problem in dynamics is `2/5` and the probability that student Y solves the same problem is `1/4`. What is the probability that
- the problem is not solved
- the problem is solved
- the problem is solved exactly by one of them
A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, the balls are of different color?
A bag contains 3 red and 5 white balls. Two balls are drawn at random one after the other without replacement. Find the probability that both the balls are white.
Solution: Let,
A : First ball drawn is white
B : second ball drawn in white.
P(A) = `square/square`
After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining `square` balls.
∴ P(B/A) = `square/square`
∴ P(Both balls are white) = P(A ∩ B)
`= "P"(square) * "P"(square)`
`= square * square`
= `square`
Solve the following:
Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find P(B)
Solve the following:
For three events A, B and C, we know that A and C are independent, B and C are independent, A and B are disjoint, P(A ∪ C) = `2/3`, P(B ∪ C) = `3/4`, P(A ∪ B ∪ C) = `11/12`. Find P(A), P(B) and P(C)
Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting 2 on the second die’. Are the events A and B independent?
If A and B are independent events such that 0 < P(A) < 1 and 0 < P(B) < 1, then which of the following is not correct?
If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of A, B) = `5/9`, then p = ______.
If A and B′ are independent events then P(A′ ∪ B) = 1 – ______.
Refer to Question 1 above. If the die were fair, determine whether or not the events A and B are independent.
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: 1 – (1 – P1)(1 – P2)
If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.
In Question 64 above, P(B|A′) is equal to ______.
If A and B′ are independent events, then P(A' ∪ B) = 1 – P (A) P(B')
If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then P(B|A) ≥ `1 - ("P"("B'"))/("P"("A"))`
If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P(At least two of A, B, C occur) = 3p2 – 2p3
If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.
One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?
E : ‘the card drawn is a spade’
F : ‘the card drawn is an ace’
One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?
E : ‘the card drawn is black’
F : ‘the card drawn is a king’
If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then
The probability of obtaining an even prime number on each die when a pair of dice is rolled is
Two events 'A' and 'B' are said to be independent if
Given two independent events, if the probability that exactly one of them occurs is `26/49` and the probability that none of them occurs is `15/49`, then the probability of more probable of the two events is ______.
The probability of the event A occurring is `1/3` and of the event B occurring is `1/2`. If A and B are independent events, then find the probability of neither A nor B occurring.
