Advertisements
Advertisements
Question
4 letters are to be posted in 4 post boxes. If any number of letters can be posted in any of the 4 post boxes, what is the probability that each box contains only one letter?
Solution
There are 4 letters and 4 post boxes.
Since any number of letters can be posted in all 4 post boxes, so each letter can be posted in 4 different ways.
∴ n(S) = 4 x 4 x 4 x 4
Let event A: Each box contains only one letter.
∴ 1st letter can be posted in 4 different ways.
Since each box contains only one letter,
2nd letter can be posted in 3 different ways.
Similarly, 3rd and 4th letters can be posted in 2 different ways and 1 way respectively.
∴ n(A) = 4 x 3 x 2 x 1
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(4 xx 3 xx 2 xx 1)/(4 xx 4 xx 4 xx 4)`
= `3/32`.
APPEARS IN
RELATED QUESTIONS
A fair die is thrown two times. Find the probability that sum of the numbers on them is 5
Two cards are drawn from a pack of 52 cards. Find the probability that one is a face card and the other is an ace card
Two cards are drawn from a pack of 52 cards. Find the probability that both are from the same suit.
Two cards are drawn from a pack of 52 cards. Find the probability that both are red cards
Two cards are drawn from a pack of 52 cards. Find the probability that one is a heart card and the other is a non-heart card
Three cards are drawn from a pack of 52 cards. Find the chance that two are queen cards and one is an ace card
Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit
Find the probability of getting both red balls, when from a bag containing 5 red and 4 black balls, two balls are drawn, with replacement
Find the probability of getting both red balls, when from a bag containing 5 red and 4 black balls, two balls are drawn, without replacement
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are never together
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement starting with a vowel and end with a consonant
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that one is black and two are red.
A bag contains 75 tickets numbered from 1 to 75. One ticket is drawn at random. Find the probability that, number on the ticket is a prime number or greater than 40
A bag contains 5 red, 4 blue and an unknown number m of green balls. If the probability of getting both the balls green, when two balls are selected at random is `1/7`, find m
Form a group of 4 men, 4 women and 3 children, 4 persons are selected at random. Find the probability that, exactly 2 men are selected
Select the correct option from the given alternatives :
There are 2 shelves. One shelf has 5 Physics and 3 Biology books and the other has 4 Physics and 2 Biology books. The probability of drawing a Physics book is
Select the correct option from the given alternatives :
The probability that a student knows the correct answer to a multiple choice question is `2/3`. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is `1/4`. Given that the student has answered the question correctly, the probability that the student knows the correct answer is
Solve the following:
An urn contains 5 red balls and 2 green balls. A ball is drawn. If its green, a red ball is added to the urn and if its red, a green ball is added to the urn. (The original ball is not returned to the urn). Then a second ball is drawn. What is the probability that the second ball is red?
Solve the following:
Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-byone, at random and without replacement. What is the probability that we are lucky and fine both of the defective fuses in the first two tests?
Solve the following:
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls given that at least one of them is a girl
If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is ______.
The probability that three cards drawn from a pack of 52 cards, all are red is ______.
A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is ______.
Four mangoes and five apples are in a box. If two fruits are chosen at random, then find the probability that one is a mango and other is an apple ______.
If two letters of the word MOTHER are selected at random. Probability that both are consonants is ______.
A cupboard contains 3 pink, 3 black and 5 blue shirts well mixed. A person pulls out 2 shirts at random from cupboard. The probability that they match is ______.
A die is rolled. If X denotes the number of positive divisors of the outcome then the range of the random variable X is ______.
A die is thrown four times. The probability of getting perfect square in at least one throw is ______.
If 15 coupons are numbered 1, 2, 3, ..., 15, respectively. 7 coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is almost 9, is ______.
The probability of India winning a test match against South Africa is 1/2 assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is ______.
