Advertisements
Advertisements
प्रश्न
If A and B are two independent events such that P (`bar A` ∩ B) = 2/15 and P (A ∩`bar B` ) = 1/6, then find P (B).
उत्तर
\[\text{ Let }: \]
\[P\left( A \right) = x \]
\[P\left( B \right) = y\]
\[P\left( \bar{A} \cap B \right) = \frac{2}{15}\]
\[ \Rightarrow P\left( \bar{A} \right) \times P\left( B \right) = \frac{2}{15}\]
\[ \Rightarrow \left( 1 - x \right)y = \frac{2}{15} . . . \left( 1 \right)\]
\[P\left( A \cap \bar{B} \right) = \frac{1}{6}\]
\[ \Rightarrow P\left( A \right) \times P\left( B \right) = \frac{1}{6} \]
\[ \Rightarrow \left( 1 - y \right)x = \frac{1}{6} . . . \left( 2 \right)\]
\[\text{ Subtracting} \left( 2 \right) \text{from} \left( 1 \right), \text{ we get } \]
\[x - y = \frac{1}{30}\]
\[x = y + \frac{1}{30}\]
\[\text {Substituting the value of x in } \left( 2 \right),\text{ we get } \]
\[\left( y + \frac{1}{30} \right)\left( 1 - y \right) = \frac{1}{6}\]
\[ \Rightarrow 30 y^2 - 29y + 4 = 0\]
\[ \Rightarrow y = \frac{1}{6}, \frac{4}{5}\]
APPEARS IN
संबंधित प्रश्न
In a shop X, 30 tins of pure ghee and 40 tins of adulterated ghee which look alike, are kept for sale while in shop Y, similar 50 tins of pure ghee and 60 tins of adulterated ghee are there. One tin of ghee is purchased from one of the randomly selected shops and is found to be adulterated. Find the probability that it is purchased from shop Y. What measures should be taken to stop adulteration?
Bag A contains 3 red and 5 black balls, while bag B contains 4 red and 4 black balls. Two balls are transferred at random from bag A to bag B and then a ball is drawn from bag B at random. If the ball drawn from bag B is found to be red find the probability that two red balls were transferred from A to B.
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4'.
From a deck of cards, three cards are drawn on by one without replacement. Find the probability that each time it is a card of spade.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that both are kings .
A bag contains 20 tickets, numbered from 1 to 20. Two tickets are drawn without replacement. What is the probability that the first ticket has an even number and the second an odd number.
An urn contains 3 white, 4 red and 5 black balls. Two balls are drawn one by one without replacement. What is the probability that at least one ball is black?
A bag contains 5 white, 7 red and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.
A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.
A die is thrown three times. Find P (A/B) and P (B/A), if
A = 4 appears on the third toss, B = 6 and 5 appear respectively on first two tosses.
Mother, father and son line up at random for a family picture. If A and B are two events given by A = Son on one end, B = Father in the middle, find P (A/B) and P (B/A).
A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
A coin is tossed thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events A and B are independent?
A = the first throw results in head, B = the last throw results in tail.
A coin is tossed thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events A and B are independent?
A = the number of heads is odd, B = the number of tails is odd.
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row. C and A
Given two independent events A and B such that P (A) = 0.3 and P (B) `= 0.6. Find P ( overlineA ∩ B) .`
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (B/A) .
A die is thrown 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 first ball is black and second is red.
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is 1/3 and that of Monika's selection is 1/5. Find the probability that
(i) both of them will be selected
(ii) none of them will be selected
(iii) at least one of them will be selected
(iv) only one of them will be selected.
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that both of them will be selected ?
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that none of them will be selected?
A bag contains 4 red and 5 black balls, a second bag contains 3 red and 7 black balls. One ball is drawn at random from each bag, find the probability that the (i) balls are of different colours (ii) balls are of the same colour.
Three persons A, B, C throw a die in succession till one gets a 'six' and wins the game. Find their respective probabilities of winning.
There are 3 red and 5 black balls in bag 'A'; and 2 red and 3 black balls in bag 'B'. One ball is drawn from bag 'A' and two from bag 'B'. Find the probability that out of the 3 balls drawn one is red and 2 are black.
The contents of three bags I, II and III are as follows:
Bag I : 1 white, 2 black and 3 red balls,
Bag II : 2 white, 1 black and 1 red ball;
Bag III : 4 white, 5 black and 3 red balls.
A bag is chosen at random and two balls are drawn. What is the probability that the balls are white and red?
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the sum of the numbers obtained is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?
Three digit numbers are formed with the digits 0, 2, 4, 6 and 8. Write the probability of forming a three digit number with the same digits.
If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P (A) + P (B) + P (C).
Three faces of an ordinary dice are yellow, two faces are red and one face is blue. The dice is rolled 3 times. The probability that yellow red and blue face appear in the first second and third throws respectively, is
An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
If S is the sample space and P (A) = \[\frac{1}{3}\]P (B) and S = A ∪ B, where A and B are two mutually exclusive events, then P (A) =
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
Choose the correct alternative in the following question: \[\text{ Let } P\left( A \right) = \frac{7}{13}, P\left( B \right) = \frac{9}{13} \text{ and } P\left( A \cap B \right) = \frac{4}{13} . \text{ Then } , P\left( \overline{ A }|B \right) = \]
Mark the correct alternative in the following question
Three persons, A, B and C fire a target in turn starting with A. Their probabilities of hitting the target are 0.4, 0.2 and 0.2, respectively. The probability of two hits is
A and B are two students. Their chances of solving a problem correctly are `1/3` and `1/4` respectively. If the probability of their making common error is `1/20` and they obtain the same answer, then the probability of their answer to be correct is
Mark the correct alternative in the following question:
If two events are independent, then
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is ______.
