Advertisements
Advertisements
Question
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
Options
\[\frac{1}{4}\]
\[\frac{11}{24}\]
\[\frac{15}{24}\]
\[\frac{23}{24}\]
Solution
4 letters can be placed in 4 envelopes in 4! ways = 24 ways
Now, there is only one method, by which all the letters are placed in the right envelope.
P(all letters are placed in the right envelopes) = \[\frac{1}{24}\] P(all letters are not placed in the right envelopes) = 1 - P(all letters are placed in the right envelopes)
\[ = \frac{23}{24}\]
APPEARS IN
RELATED QUESTIONS
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 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.
Bag A contains 3 red and 5 black balls, while bag B contains 4 red and 4 black balls. Two balls are transferred at random from bag A to bag B and then a ball is drawn from bag B at random. If the ball drawn from bag B is found to be red find the probability that two red balls were transferred from A to B.
If A and B are two events such that P (A) = \[\frac{1}{3},\] P (B) = \[\frac{1}{5}\] and P (A ∪ B) = \[\frac{11}{30}\] , find P (A/B) and P (B/A).
From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.
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 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 \[ P\left( A \right) = \frac{1}{3}, P\left( B \right) = \frac{1}{4} \text{ and } P\left( A \cup B \right) = \frac{5}{12}, \text{ then find } P\left( A|B \right) \text{ and } P\left( B|A \right) . \]
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.
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.
Two dice are thrown and it is known that the first die shows a 6. Find the probability that the sum of the numbers showing on two dice is 7.
Prove that in throwing a pair of dice, the occurrence of the number 4 on the first die is independent of the occurrence of 5 on the second die.
If A and B are two independent events such that P (`bar A` ∩ B) = 2/15 and P (A ∩`bar B` ) = 1/6, then find P (B).
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.
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.
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.
A and B take turns in throwing two dice, the first to throw 10 being awarded the prize, show that if A has the first throw, their chance of winning are in the ratio 12 : 11.
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.
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 bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
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.
A bag contains 6 red and 8 black balls and another bag contains 8 red and 6 black balls. A ball is drawn from the first bag and without noticing its colour is put in the second bag. A ball is drawn from the second bag. Find the probability that the ball drawn is red in colour.
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.
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, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P (A) + P (B) + P (C).
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
Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is
If A and B are two events, then P (`overline A` ∩ B) =
Mark the correct alternative in the following question:
If A and B are two events such that P(A) = \[\frac{4}{5}\] , and \[P\left( A \cap B \right) = \frac{7}{10}\] , then P(B|A) =
Mark the correct alternative in the following question:
\[ \text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( \overline{A \cup B }\right) = \frac{4}{5}, \text{ then } P\left( \overline{ A } \cup B \right) + P\left( A \cup B \right) = \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two independent events with } P\left( A \right) = \frac{3}{5} \text{ and } P\left( B \right) = \frac{4}{9}, \text{ then } P\left( \overline{A} \cap B \right) \text{ equals } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two independent events such that} P\left( A \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( A|B \right) - P\left( B|A \right) = \]
Mark the correct alternative in the following question: A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red ball is
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
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
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.
