Advertisements
Advertisements
प्रश्न
If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?
उत्तर
Word ALGORITHM has 9 letters.
If GOR remain together, then it will remain together.
∴ Number of letters = ALGOR ITHM = 6 + 1 = 7
Number of words = 7!
And the total number of words from ALGORITHM = 9!
So, the required probability = `(71)/(9!)`
= `(7!)/(9*8*7!)`
= `1/72`
Hence, the required probability = `1/72`.
APPEARS IN
संबंधित प्रश्न
Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {ω1, ω2,ω3,ω4,ω5,ω6,ω7}
| Assignment | ω1 | ω2 | ω3 | ω4 | ω5 | ω6 | ω7 |
| (a) | 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |
| (b) | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` |
| (c) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
| (d) | –0.1 | 0.2 | 0.3 | 0.4 | -0.2 | 0.1 | 0.3 |
| (e) | `1/14` | `2/14` | `3/14` | `4/14` | `5/14` | `6/14` | `15/14` |
A coin is tossed twice, what is the probability that at least one tail occurs?
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?
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.35 | ... | 0.25 | 0.6 |
4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
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?
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, the digits are repeated?
A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.
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 |
| (i) | 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |
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 thatat least one is defective
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that none is defective
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 blue or white
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
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 white and numbered higher than 12 or yellow and numbered higher than 26.
One mapping (function) is selected at random from all the mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is ______.
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(A)
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 one ball is red and two balls are white
If the letters of the word ASSASSINATION are arranged at random. Find the probability that four S’s come consecutively in the word
In a non-leap year, the probability of having 53 tuesdays or 53 wednesdays 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 ______.
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?
