Advertisements
Advertisements
प्रश्न
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.
उत्तर
\[ P\left( \text{ black } \right) = P\left( A \right) = \frac{26}{52} = \frac{1}{2}\]
\[P\left( \text{ king } \right) = P\left( B \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( A \cap B \right) = P\left( \text{ black king } \right) = \frac{2}{52} = \frac{1}{26}\]
\[P\left( A \cap B \right) = P\left( A \right) P\left( B \right)\]
\[\text{ Thus, A and B are independent events } .\]
APPEARS IN
संबंधित प्रश्न
How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?
Find the chance of drawing 2 white balls in succession from a bag containing 5 red and 7 white balls, the ball first drawn not being replaced.
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 events such that P (A) = 0.6, P (B) = 0.3 and P (A ∩ B) = 0.2, find P (A/B) and P (B/A).
If A and B are two events such that \[ P\left( A \right) = \frac{7}{13}, P\left( B \right) = \frac{9}{13} \text{ and } P\left( A \cap B \right) = \frac{4}{13}, \text{ then find } P\left( \overline{ A }|B \right) . \]
If A and B are two events such that
\[ P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cap B \right) = \frac{1}{4}, \text{ then find } P\left( A|B \right), P\left( B|A \right), P\left( \overline{ A }|B \right) \text{ and } P\left( \overline{ A }|\overline{ B } \right) .\]
A coin is tossed three times. Find P (A/B) in each of the following:
A = At most two tails, B = At least one tail.
Two numbers are selected at random from integers 1 through 9. If the sum is even, find the probability that both the numbers are 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 a king or queen, B = the card drawn is a queen or jack.
If A and B be two events such that P (A) = 1/4, P (B) = 1/3 and P (A ∪ B) = 1/2, show that A and B are independent events.
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
Given the probability that A can solve a problem is 2/3 and the probability that B can solve the same problem is 3/5. Find the probability that none of the two will be able to solve the problem.
Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.
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.
In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.
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?
There are three urns A, B, and C. Urn A contains 4 red balls and 3 black balls. urn B contains 5 red balls and 4 black balls. Urn C contains 4 red and 4 black balls. One ball is drawn from each of these urns. What is the probability that 3 balls drawn consists of 2 red balls and a black ball?
A bag A contains 5 white and 6 black balls. Another bag B contains 4 white and 3 black balls. A ball is transferred from bag A to the bag B and then a ball is taken out of the second bag. Find the probability of this ball being black.
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?
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.
One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.
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.
An unbiased die with face marked 1, 2, 3, 4, 5, 6 is rolled four times. Out of 4 face values obtained, find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5.
If A and B are two events write the expression for the probability of occurrence of exactly one of two events.
If A and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).
If P (A) = 0.3, P (B) = 0.6, P (B/A) = 0.5, find P (A ∪ B).
If A and B are independent events, then write expression for P(exactly one of A, B occurs).
A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement, 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
A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is
A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability chosen to be white 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
Mark the correct alternative in the following question:
\[\text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( A \cup B \right) = \frac{4}{5}, \text{ then } P\left( B|\overline{ A } \right) = \]
Mark the correct alternative in the following question:A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then the probability that both are dead is
Mark the correct alternative in the following question:
\[\text{ Let A and B be two events such that P } \left( A \right) = 0 . 6, P\left( B \right) = 0 . 2, P\left( A|B \right) = 0 . 5 . \text{ Then } P\left( \overline{A}|\overline{B} \right) \text{ equals } \]
A coin is tossed 5 times. Find the probability of getting (i) at least 4 heads, and (ii) at most 4 heads.
Out of 8 outstanding students of a school, in which there are 3 boys and 5 girls, a team of 4 students is to be selected for a quiz competition. Find the probability that 2 boys and 2 girls are selected.
A and B throw a die alternately till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts the game first.
