Advertisements
Advertisements
Question
Mark the correct alternative in the following question:
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability that both cards are queen is
Options
\[ \frac{1}{13} \times \frac{1}{13}\]
\[\frac{1}{13} + \frac{1}{13}\]
\[\frac{1}{13} \times \frac{1}{17}\]
\[\frac{1}{13} \times \frac{4}{5}\]
Solution
\[\text{ Let } : \]
\[\text{ A be the event that a queen is drawn in the first draw and } \]
\[\text{ B be the event that a queen is drawn in the second draw as well} \]
\[\text{ Now } , \]
\[P\left( \text{ Both the two cards drawn are queen } \right) = P\left( A \right) \times P\left( B|A \right)\]
\[ = \frac{4}{52} \times \frac{4}{52}\]
\[ = \frac{1}{13} \times \frac{1}{13}\]
APPEARS IN
RELATED QUESTIONS
In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides.
How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?
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?
A coin is tossed three times, if head occurs on first two tosses, find the probability of getting head on third toss.
A die is thrown three times, find the probability that 4 appears on the third toss if it is given that 6 and 5 appear respectively on first two tosses.
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.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that the first is a king and the second is an ace.
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.
If P (A) = \[\frac{7}{13}\], P (B) = \[\frac{9}{13}\] and P (A ∩ B) = \[\frac{4}{13}\], find P (A/B).
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 P (A) = \[\frac{6}{11},\] P (B) = \[\frac{5}{11}\] and P (A ∪ B) = \[\frac{7}{11},\] find
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.
A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
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. B and C .
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A ∪ 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 anti-aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
The odds against a certain event are 5 to 2 and the odds in favour of another event, independent to the former are 6 to 5. Find the probability that (i) at least one of the events will occur, and (ii) none of the events will occur.
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: p1 + p2 - 2p1p2
A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that both the balls are red.
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 only one of them will be selected ?
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.
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.
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.
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 bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is black or red ball is
A coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head. Then, A and B are ______.
If A and B are two events, then P (`overline A` ∩ B) =
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
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
Mark the correct alternative in the following question:
\[ \text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( \overline{A \cup B }\right) = \frac{4}{5}, \text{ then } P\left( \overline{ A } \cup B \right) + P\left( A \cup B \right) = \]
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
Mother, father and son line up at random for a family photo. If A and B are two events given by
A = Son on one end, B = Father in the middle, find P(B / A).
There are two boxes I and II. Box I contains 3 red and 6 Black balls. Box II contains 5 red and black balls. One of the two boxes, box I and box II is selected at random and a ball is drawn at random. The ball drawn is found to be red. If the probability that this red ball comes out from box II is ' a find the value of n
