Advertisements
Advertisements
प्रश्न
If the letters of the word ASSASSINATION are arranged at random. Find the probability that all A’s are not coming together
Advertisements
उत्तर
Total number of word is ASSASSINATION are 13.
Where, we have 3A’s, 4S’, 2I’s, 2N’s, 1T’s and 1O’s.
If all A’s are coming together, then three are 11 alphabets
Number of words when all A’s come together
= `(11!)/(4!2!2!)`
∴ Probability when all A’s come together
= `((11!)/(4!2!2!))/((13!)/(4!3!2!2!))`
= `(11!)/(4!2!2!) xx (4!3!2!2!)/(13!)`
= `(11! xx 3!)/(13!)`
= `6/(13 xx 12)`
= `1/26`
∴ Required probability when all A’s do not come together
= `1 - 1/26 = 25/26`
APPEARS IN
संबंधित प्रश्न
A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12
There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
Check whether the following probabilities P(A) and P(B) are consistently defined
P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.35 | ... | 0.25 | 0.6 |
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.5 | 0.35 | .... | 0.7 |
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:
| S. No. | Name | Sex | Age in years |
| 1. | Harish | M | 30 |
| 2. | Rohan | M | 33 |
| 3. | Sheetal | F | 46 |
| 4. | Alis | F | 28 |
| 5. | Salim | M | 41 |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that all the three balls are blue balls
If a letter is chosen at random from the English alphabet, find the probability that the letter is a vowel .
If a letter is chosen at random from the English alphabet, find the probability that the letter is a consonant .
Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S = {w1, w2, w3, w4, w5, w6, w7}:
| Elementary events: | w1 | w2 | w3 | w4 | w5 | w6 | w7 |
| (ii) |
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
In a single throw of three dice, find the probability of getting the same number on all the three dice.
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that all 10 are good
Two dice are thrown together. The probability that neither they show equal digits nor the sum of their digits is 9 will be
An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is numbered 1, 2, 3, 4 or 5
An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is red or yellow and numbered 1, 2, 3 or 4
In a leap year the probability of having 53 Sundays or 53 Mondays is ______.
Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?
Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that A will not be selected?
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine P(B ∩ C)
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine Probability of exactly one of the three occurs
A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that all the three balls are white
A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that all the three balls are red
A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that all one ball is red and two balls are white
In a non-leap year, the probability of having 53 tuesdays or 53 wednesdays is ______.
A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is ______.
If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is ______.
The probability that a person visiting a zoo will see the giraffee is 0.72, the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52.
If A and B are two candidates seeking admission in an engineering College. The probability that A is selected is .5 and the probability that both A and B are selected is at most .3. Is it possible that the probability of B getting selected is 0.7?
The sum of probabilities of two students getting distinction in their final examinations is 1.2
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is ______.
| C1 Probability |
C2 Written Description |
| (a) 0.95 | (i) An incorrect assignment |
| (b) 0.02 | (ii) No chance of happening |
| (c) – 0.3 | (iii) As much chance of happening as not |
| (d) 0.5 | (iv) Very likely to happen |
| (e) 0 | (v) Very little chance of happening |
