Advertisements
Advertisements
प्रश्न
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( B \cap A \right) \text{ equals } \]
विकल्प
\[\frac{2}{3}\]
\[ \frac{1}{2}\]
\[ \frac{3}{10}\]
\[ \frac{1}{5}\]
उत्तर
\[\text{ We have, } \]
\[P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5\]
\[\text{ As }, P\left( A \cup B \right) = 0 . 5\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) - P\left( A \cap B \right) = 0 . 5\]
\[ \Rightarrow 0 . 4 + 0 . 3 - P\left( A \cap B \right) = 0 . 5\]
\[ \Rightarrow 0 . 7 - P\left( A \cap B \right) = 0 . 5\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 7 - 0 . 5\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 2\]
\[\text{ Now} , \]
\[P\left(\overline{ B } \cap A \right) = P\left( A \right) - P\left( A \cap B \right)\]
\[ = 0 . 4 - 0 . 2\]
\[ = 0 . 2\]
\[ = \frac{2}{10}\]
\[ = \frac{1}{5}\]
APPEARS IN
संबंधित प्रश्न
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins
An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
(i) 5 successes?
(ii) at least 5 successes?
(iii) at most 5 successes?
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that the first is a heart and second is red.
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.
If A and B are two events such that P (A ∩ B) = 0.32 and P (B) = 0.5, find P (A/B).
If P (A) = 0.4, P (B) = 0.8, P (B/A) = 0.6. Find P (A/B) and P (A ∪ B).
If A and B are two events such that 2 P (A) = P (B) = \[\frac{5}{13}\] and P (A/B) = \[\frac{2}{5},\] 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 = Heads on third toss, B = Heads on first two tosses.
Two coins are tossed once. Find P (A/B) in each of the following:
A = Tail appears on one coin, B = One coin shows head.
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
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 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 black, B = the card drawn is a king.
Given two independent events A and B such that P (A) = 0.3 and P (B) `= 0.6. Find P ( overlineA ∩ B) .`
An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part Y. Calculate the probability that the assembled product will not be defective.
An urn contains 4 red and 7 black balls. Two balls are drawn at random with replacement. Find the probability of getting 2 red balls.
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are: `1 - (1 - p_1 )(1 -p_2 ) `
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.
A and B toss a coin alternately till one of them gets a head and wins the game. If A starts the game, find the probability that B will win the game.
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 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?
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
A purse contains 2 silver and 4 copper coins. A second purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin?
A bag contains 4 white and 5 black balls and another bag contains 3 white and 4 black balls. A ball is taken out from the first bag and without seeing its colour is put in the second bag. A ball is taken out from the latter. Find the probability that the ball drawn is white.
An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. Two are drawn from first urn and put into the second urn and then a ball is drawn from the latter. Find the probability that its is a white ball.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is
A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
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
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
Two persons A and B take turns in throwing a pair of dice. The first person to throw 9 from both dice will be awarded the prize. If A throws first, then the probability that Bwins the game is
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:
\[\text{ If } P\left( A \right) = \frac{2}{5}, P\left( B \right) = \frac{3}{10} \text{ and } P\left( A \cap B \right) = \frac{1}{5}, \text{ then } , P\left( \overline { A }|\overline{ B } \right) P\left( \overline{ B }|\overline{ A } \right) \text{ is equal to } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3}, P\left( A|B \right) = \frac{1}{4}, \text{ then } P\left( A \cap B \right) \text{ equals} \]
Mark the correct alternative in the following question:
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is ______.
A coin is tossed 5 times. Find the probability of getting (i) at least 4 heads, and (ii) at most 4 heads.
A, B and C throw a pair of dice in that order alternatively till one of them gets a total of 9 and wins the game. Find their respective probabilities of winning, if A starts first.
