Advertisements
Advertisements
प्रश्न
Mark the correct alternative in the following question:
\[\text{ If A and B are two independent events such that} P\left( A \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( A|B \right) - P\left( B|A \right) = \]
विकल्प
\[ \frac{2}{7}\]
\[ \frac{3}{35}\]
\[ \frac{1}{70} \]
\[ \frac{1}{7}\]
उत्तर
\[\text{ We have } , \]
\[P\left( A \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5\]
\[\text{ As, A and B are independent events} \]
\[\text{ So } , P\left( A \cap B \right) = P\left( A \right) \times P\left( B \right)\]
\[ = 0 . 3 \times P\left( B \right)\]
\[ = 0 . 3P\left( B \right) . . . . . \left( i \right)\]
\[\text{ Also} , P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow 0 . 5 = 0 . 3 + P\left( B \right) - 0 . 3P\left( B \right) \left[ \text{Using } \left( i \right) \right]\]
\[ \Rightarrow 0 . 5 - 0 . 3 = 0 . 7P\left( B \right)\]
\[ \Rightarrow 0 . 7P\left( B \right) = 0 . 2\]
\[ \Rightarrow P\left( B \right) = \frac{0 . 2}{0 . 7}\]
\[ \Rightarrow P\left( B \right) = \frac{2}{7}\]
\[\text{ Using } \left( i \right), \text{ we get } \]
\[P\left( A \cap B \right) = 0 . 3 \times \frac{2}{7} = \frac{6}{70}\]
\[\text{ Now } , \]
\[P\left( A|B \right) - P\left( B|A \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)} - \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ = \frac{\left( \frac{6}{70} \right)}{\left( \frac{2}{7} \right)} - \frac{\left( \frac{6}{70} \right)}{0 . 3}\]
\[ = \frac{6 \times 7}{70 \times 2} - \frac{6}{70 \times 0 . 3}\]
\[ = \frac{3}{10} - \frac{2}{7}\]
\[ = \frac{21 - 20}{70}\]
\[ = \frac{1}{70}\]
APPEARS IN
संबंधित प्रश्न
A and B throw a die alternatively till one of them gets a number greater than four and wins the game. If A starts the game, what is the probability of B winning?
A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first
A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B, If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale otherwise it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.
If P (A) = \[\frac{7}{13}\], P (B) = \[\frac{9}{13}\] and P (A ∩ B) = \[\frac{4}{13}\], find P (A/B).
If P (A) = \[\frac{6}{11},\] P (B) = \[\frac{5}{11}\] and P (A ∪ B) = \[\frac{7}{11},\] find
A coin is tossed three times. Find P (A/B) in each of the following:
A = At least two heads, B = At most two heads
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 pair of dice is thrown. Find the probability of getting 7 as the sum if it is known that the second die always exhibits a prime number.
A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 and F be the event "5 appears on the first-die". Find P (E/F). If F is the event "5 appears on at least one die", find P (E/F).
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, then what is the constitutional probability that both are girls? Given that
(i) the youngest is a girl (b) at least one is a girl.
A card is drawn from a pack of 52 cards so the teach card is equally likely to be selected. In which of the following cases are the events A and B independent?
A = The card drawn is a king or queen, B = the card drawn is a queen or jack.
Given two independent events A and B such that P (A) = 0.3 and P (B) = `0.6. Find P (A ∩ overlineB ) `.
A bag contains 3 red and 2 black balls. One ball is drawn from it at random. Its colour is noted and then it is put back in the bag. A second draw is made and the same procedure is repeated. Find the probability of drawing (i) two red balls, (ii) two black balls, (iii) first red and second black ball.
A die is thrown thrice. Find the probability of getting an odd number at least once.
An urn contains 4 red and 7 black balls. Two balls are drawn at random with replacement. Find the probability of getting 2 blue balls.
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.
A can hit a target 3 times in 6 shots, B : 2 times in 6 shots and C : 4 times in 4 shots. They fix a volley. What is the probability that at least 2 shots hit?
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?
A factory has two machines A and B. Past records show that the machine A produced 60% of the items of output and machine B produced 40% of the items. Further 2% of the items produced by machine A were defective and 1% produced by machine B were defective. If an item is drawn at random, what is the probability that it is defective?
The bag A contains 8 white and 7 black balls while the bag B contains 5 white and 4 black balls. One ball is randomly picked up from the bag A and mixed up with the balls in bag B. Then a ball is randomly drawn out from it. Find the probability that ball drawn is white.
Three machines E1, E2, E3 in a certain factory produce 50%, 25% and 25%, respectively, of the total daily output of electric bulbs. It is known that 4% of the tubes produced one each of the machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day's production, then calculate the probability that it is defective.
Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.
If A and B are two events write the expression for the probability of occurrence of exactly one of two events.
Write the probability that a number selected at random from the set of first 100 natural numbers is a cube.
If A and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).
If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of Aand B occurs) = \[\frac{5}{9}\], then find the value of p.
The probabilities of a student getting I, II and III division in an examination are \[\frac{1}{10}, \frac{3}{5}\text{ and } \frac{1}{4}\]respectively. The probability that the student fails in the examination is
India play two matches each with West Indies and Australia. In any match the probabilities of India getting 0,1 and 2 points are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is
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
A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
Mark the correct alternative in the following question:
\[ \text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( \overline{A \cup B }\right) = \frac{4}{5}, \text{ then } P\left( \overline{ A } \cup B \right) + P\left( A \cup B \right) = \]
If A and B are two events such that A ≠ Φ, B = Φ, then
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
Mark the correct alternative in the following question:
Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is ______.
An insurance company insured 3000 cyclists, 6000 scooter drivers, and 9000 car drivers. The probability of an accident involving a cyclist, a scooter driver, and a car driver are 0⋅3, 0⋅05 and 0⋅02 respectively. One of the insured persons meets with an accident. What is the probability that he is a cyclist?
