Advertisements
Advertisements
प्रश्न
Events A and Bare such that P(A) = `1/2`, P(B) = `7/12` and `P(barA ∪ barB) = 1/4`. Find whether the events A and B are independent or not.
Advertisements
उत्तर
Given, P(A) = `1/2`, P(B) = `7/12`
And `P(barA ∪ barB) = 1/4`
For A and B are independent
P(A ∩ B) = P(A).P(B) ...(i)
Now, `P(barA ∪ barB)` = P(A ∩ B)
⇒ `P(barA ∪ barB)` = 1 – P(A ∩ B)
⇒ P(A ∩ B) = `1 - P(barA ∪ barB)`
⇒ P(A ∩ B) = `1 - 1/4 = 3/4` ...(ii)
Now, P(A).P(B) = `1/2 xx 7/12 = 7/24` ...(iii)
Since from equations (ii) and (ill)
P(A ∩ B) ≠ P(A).P(B)
Therefore, events A and B are not independent.
APPEARS IN
संबंधित प्रश्न
A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white?
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
Two events, A and B, will be independent if ______.
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.
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'.
The odds against a certain event are 5: 2 and odds in favour of another independent event are 6: 5. Find the chance that at least one of the events will happen.
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.
Select the correct option from the given alternatives :
The odds against an event are 5:3 and the odds in favour of another independent event are 7:5. The probability that at least one of the two events will occur is
Solve the following:
If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"B")`
Solve the following:
If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("B'"/"A'")`
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:
A and B throw a die alternatively till one of them gets a 3 and wins the game. Find the respective probabilities of winning. (Assuming A begins the game)
10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.
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?
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
If the events A and B are independent, then P(A ∩ B) is equal to ______.
If A and B are two independent events then P(A and B) = P(A).P(B).
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
Let Bi(i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β and only B3 occurs is γ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α – 2β)p = αβ and (β – 3γ) = 2βy (All the probabilities are assumed to lie in the interval (0, 1)). Then `("P"("B"_1))/("P"("B"_3))` is equal to ______.
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 ______.
Let E and F be two independent events. The probability that both E and F happen is `1/12` and the probability that neither E nor F happens is `1/2`, then a value of `(P(E))/(P(F))` is ______.
Two events E and F are independent when which conditional probability condition holds, provided \[P(E) \ne 0\]?
If E and F are independent, which pair is also independent?
A die is thrown once. If E is the event that the number appearing is a multiple of 3, which set represents E?
A die is thrown once. If F is the event that the number appearing is even, which set represents F?
For \[E=\{3,6\}\] when a die is thrown once, what is \[P(E)\]?
For \[F=\{2,4,6\}\] when a die is thrown once, what is \[P(F)\]?
For \[E\cap F=\{6\}\] when a die is thrown once, what is \[P(E\cap F)\]?
