Advertisements
Advertisements
प्रश्न
A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.
Advertisements
उत्तर
Bag X = 4 white, 2 black.
Bag Y = 3 white, 3 black
Let A be the event of selecting one white and one black ball.
E1 first bag selected
E2 second bag selected
`P(E_1)=1/2 P(E_2)=1/2`
`P(A/E_1)=4/6xx2/5+2/6xx4/5=16/30`
`P(AE_2)=3/6xx3/5+3/6xx3/6xx3/5=18/30`
`P(E_2"/"A)=(P(E_2)P(A"/"E_2))/(P(E_1)P(A"/"E_1)+P(E_2)P(A"/"E_2)`
`P(E_2"/"A)= (1/2xx18/30)/(1/2xx16/30+1/2xx18/30)`
`=18/(16+18)`
=`18/34`
=`9/17`
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(A ∪ B)
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)|G) and P ((E ∩ G)|G)
A die is tossed thrice. Find the probability of getting an odd number at least once.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
- both balls are red.
- first ball is black and second is red.
- one of them is black and other is red.
In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.
Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.
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 first card drawn is kept aside
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
If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)
If for two events A and B, P(A) = `3/4`, P(B) = `2/5` and A ∪ B = S (sample space), find the conditional probability P(A/B)
The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?
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.
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is ______.
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 ______.
If A and B are two independent events such that P(A) = `1/3` and P(B) = `1/4`, then `P(B^'/A)` is ______.
If P(B) = `3/5`, P(A | B) = `1/2` and P(A ∪ B) = `4/5`, then P(A ∪ B) + P(A' ∪ B) =
For independent events, which equality holds provided \[P(B)\neq 0\]?
