Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
Given, P(L) = `12/100`
`P(L) P(overlineL) = 1 - 12/100 = 88/100`
and P(A) = P(B) = P(C) = P(D) = `1/4`
`P(L/A) = 24/100`,
`P(L/B) = 22/100`,
`P(L/C) = 17/100`,
`P(L/D) = 9/100`
(i) `P(L/C) = 17/100`, from the given data.
(ii) `P(overlineL/A) = (P(overlineL ∩ A))/(P(A))`
= `(P(A) - P(L ∩ A))/(P(A))`
= `1 - (P(L ∩ A))/(P(A))`
= `1 - P(L/A)`
= `1 - 24/100`
= `(100 - 24)/100`
= `76/100`
= `38/50`
= `19/25`
(iii) (a) `P(A/L) = (P(A ∩ L))/(P(L))`
But `P(L/A) = (P(A ∩ L))/(P(A))`
`24/100 = (P(A ∩ L))/(1/4)`
`\implies` P(A ∩ L) = `24/100 xx 1/4 = 6/100 = 3/50`
∴ `P(A/L) = (3/50)/(12/100) = (3 xx 100)/(12 xx 50) = 1/2`.
OR
(b) `P(L/(B ∪ C)) = (P[(L) ∩ (B ∪ C)])/(P(B ∪ C))`
= `(P[(L ∩ B) ∪ (L ∩ C)])/(P(B ∪ C))`
= `(P(L ∩ B) + P(L ∩ C) - P(L ∩ B)P(L ∩ C))/(P(B) + P(C) - P(B)P(C))` ...(As they are independent)
= `(22/100 xx 1/4 + 17/100 xx 1/4 - 22/400 xx 17/400)/(1/4 + 1/4 - 1/4 xx 1/4)`
= `(22/400 + 17/400 - (22 xx 17)/(400 xx 400))/(1/2 - 1/16)`
= `((39/400 - 374/160000))/(1/2 - 1/16)`
= `16/7((39 xx 400 - 374)/160000)`
= `(16 xx 15226)/(7 xx 160000)`
= 0.217
= 0.22
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses
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.
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)
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|G) and P (G|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’.
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.
If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
If A and B are events such as that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`, then find
1) P(A / B)
2) P(B / A)
An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball is drawn is black.
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?
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.
Three cards are drawn at random (without replacement) from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of red cards. Hence, find the mean of the distribution.
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
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)
A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that the problem is solved?
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events
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?
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
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 ______.
For a biased dice, the probability for the different faces to turn up are
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| P | 0.10 | 0.32 | 0.21 | 0.15 | 0.05 | 0.17 |
The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.
If for any two events A and B, P(A) = `4/5` and P(A ∩ B) = `7/10`, then `P(B/A)` is equal to ______.
