Advertisements
Advertisements
Question
Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?
Solution
\[P\left( \text{ one red and one black } \right) = P\left(\text{ first red and second black } \right) + P\left( \text{ first black and second red } \right)\]
\[ = \frac{26}{52} \times \frac{26}{51} + \frac{26}{52} \times \frac{26}{51} \left[ \text{ Without replacement } \right]\]
\[ = \frac{13}{51} + \frac{13}{51}\]
\[ = \frac{26}{51}\]
APPEARS IN
RELATED QUESTIONS
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 the first is a heart and second is red.
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) = 0.4, P (B) = 0.8, P (B/A) = 0.6. Find P (A/B) and P (A ∪ B).
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.
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).
Two dice are thrown. Find the probability that the numbers appeared has the sum 8, if it is known that the second die always exhibits 4.
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 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?
The probability that a certain person will buy a shirt is 0.2, the probability that he will buy a trouser is 0.3, and the probability that he will buy a shirt given that he buys a trouser is 0.4. Find the probability that he will buy both a shirt and a trouser. Find also the probability that he will buy a trouser given that he buys a shirt.
Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?
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 \[P \overline A \cup \overline B \] .
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (B/A) .
A and B are two independent events. The probability that A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of two events.
The probability that A hits a target is 1/3 and the probability that B hits it, is 2/5, What is the probability that the target will be hit, if each one of A and B shoots at the target?
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?
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red, (ii) first ball is black and second is red, (iii) one of them is black and other is red.
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.
Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.
Arun and Tarun appeared for an interview for two vacancies. The probability of Arun's selection is 1/4 and that to Tarun's rejection is 2/3. Find the probability that at least one of them will be selected.
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, B, and C are independent witness of an event which is known to have occurred. Aspeaks the truth three times out of four, B four times out of five and C five times out of six. What is the probability that the occurrence will be reported truthfully by majority of three witnesses?
Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.
X is taking up subjects - Mathematics, Physics and Chemistry in the examination. His probabilities of getting grade A in these subjects are 0.2, 0.3 and 0.5 respectively. Find the probability that he gets
(i) Grade A in all subjects
(ii) Grade A in no subject
(iii) Grade A in two subjects.
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.
An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting
(i) 2 red balls
(ii) 2 blue balls
(iii) One red and one blue ball.
A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.
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.
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
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
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:
\[\text{ If the events A and B are independent, then } P\left( A \cap B \right) \text{ is equal to } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two independent events such that} P\left( A \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( A|B \right) - P\left( B|A \right) = \]
From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24 is
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.
