Advertisements
Advertisements
Question
A person write 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
1/4
11/24
15/24
23/24
Advertisements
Solution
\[\frac{23}{24}\] Total number of ways of placing four letters in 4 envelops = 4! = 24
All the letters can be dispatched in the right envelops in only one way. Therefore, the probability that all the letters are placed in the right envelops is \[\frac{1}{24}\] .
Hence, probability that all the letters are not placed in the right envelops = \[1 - \frac{1}{24} = \frac{23}{24}\]
APPEARS IN
RELATED QUESTIONS
If `2/11` is the probability of an event, what is the probability of the event ‘not A’.
A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is
- a vowel
- an consonant
If E and F are events such that P(E) = `1/4`, P(F) = `1/2` and P(E and F) = `1/8`, find
- P(E or F)
- P(not E and not F).
A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P (not B)
In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that
- you both enter the same sections?
- you both enter the different sections?
Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
In a simultaneous throw of a pair of dice, find the probability of getting a doublet of odd numbers
In a simultaneous throw of a pair of dice, find the probability of getting an even number on one and a multiple of 3 on the other
In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 6
In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 7
In a simultaneous throw of a pair of dice, find the probability of getting a number greater than 4 on each die
Three coins are tossed together. Find the probability of getting at least one head and one tail.
What are the odds in favour of getting a spade if the card drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that all are blue?
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that at least one is green?
A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is even numbered
A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is red or even numbered.
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| \[\frac{1}{3}\] | \[\frac{1}{5}\] | \[\frac{1}{15}\] | ...... |
If A and B are two events associated with a random experiment such that
P (A ∪ B) = 0.8, P (A ∩ B) = 0.3 and P \[(\bar{A} )\]= 0.5, find P(B).
One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.
A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.
100 students appeared for two examination, 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.
Find the probability of getting 2 or 3 tails when a coin is tossed four times.
The probability that a leap year will have 53 Fridays or 53 Saturdays is
A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, 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
Two dice are thrown simultaneously. The probability of getting a pair of aces is
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect 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
Three numbers are chosen from 1 to 20. The probability that they are not consecutive is
In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets.
In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy 10 tickets.
