Advertisements
Advertisements
Question
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'.
Advertisements
Solution
If A and B are independent events, then
\[P\left( A \cap B \right) = P\left( A \right)P\left( B \right)\]
\[ \therefore P\left( A \cap B \right) = 0 . 4p \left[ \because P\left( A \right) = 0 . 4 \text { and }P\left( B \right) = p \right]\]
As P(A ⋃ B) = 0·6
So,
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow 0 . 6 = 0 . 4 + p - 0 . 4p\]
\[ \Rightarrow 0 . 2 = 0 . 6p\]
\[ \Rightarrow p = \frac{1}{3}\]
APPEARS IN
RELATED QUESTIONS
Let E and F be events with `P(E) = 3/5, P(F) = 3/10 and P(E ∩ F) = 1/5`. Are E and F independent?
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).
Events A and B are such that `P(A) = 1/2, P(B) = 7/12 and P("not A or not B") = 1/4` . State whether A and B are independent?
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`).
In a race, the probabilities of A and B winning the race are `1/3` and `1/6` respectively. Find the probability of neither of them winning the race.
The probabilities of solving a specific problem independently by A and B are `1/3` and `1/5` respectively. If both try to solve the problem independently, find the probability that the problem is solved.
A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2` and `5/8`. Find the probability that the target
- is hit exactly by one of them
- is not hit by any one of them
- is hit
- is exactly hit by two of them
Solve the following:
If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"B")`
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'"/"A")`
Solve the following:
Find the probability that a year selected will have 53 Wednesdays
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?
The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate `"P"(bar"A") + "P"(bar"B")`
Three events A, B and C have probabilities `2/5, 1/3` and `1/2`, , respectively. Given that P(A ∩ C) = `1/5` and P(B ∩ C) = `1/4`, find the values of P(C|B) and P(A' ∩ C').
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 – P1) P2
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)
A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals ______.
If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals ______.
Let A and B be two events such that P(A) = `3/8`, P(B) = `5/8` and P(A ∪ B) = `3/4`. Then P(A|B).P(A′|B) is equal to ______.
If A and B are two independent events then P(A and B) = P(A).P(B).
If A and B′ are independent events, then P(A' ∪ B) = 1 – P (A) P(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 spade’
F : ‘the card drawn is an ace’
If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then
Two events 'A' and 'B' are said to be independent if
The probability that A hits the target is `1/3` and the probability that B hits it, is `2/5`. If both try to hit the target independently, find the probability that the target is hit.
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.
Given two events A and B such that (A/B) = 0.25 and P(A ∩ B) = 0.12. The value P(A ∩ B') is ______.
Two players A and B are alternately throwing a coin and a die together. A player who first throws head and 6 wins the game. If A starts the game, then the probability that B wins the game is ______.
If E and F are independent, which pair is also independent?
A die is thrown once. What is the sample space \[S\]?
