Advertisements
Advertisements
Question
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?
Solution
Number of desk occupied by one couple = 1
Only (4 + 1) = 5 persons to be assigned.
∴ Number of ways of assigning these 5 persons = 5! × 2!
Total number of ways of assigning 6 persons = 6!
∴ Probability that a couple has adjacent desk = `(5! xx 2!)/(6!) = 1/3`
So, the probability that the married couple will have no-adjacent desks = `1 - 1/3 = 2/3`.
Hence, the required probability = `2/3`.
APPEARS IN
RELATED QUESTIONS
A coin is tossed twice, what is the probability that at least one tail occurs?
A card is selected from a pack of 52 cards.
- How many points are there in the sample space?
- Calculate the probability that the card is an ace of spades.
- Calculate the probability that the card is
- an ace
- black card.
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
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.5 | 0.35 | .... | 0.7 |
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?
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.
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 |
| (iv) |
\[\frac{1}{14}\]
|
\[\frac{2}{14}\]
|
\[\frac{3}{14}\]
|
\[\frac{4}{14}\]
|
\[\frac{5}{14}\]
|
\[\frac{6}{14}\]
|
\[\frac{15}{14}\]
|
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability thatat least one is defective
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 numbered 5, 15, 25, or 35
In a leap year the probability of having 53 Sundays or 53 Mondays is ______.
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 ______.
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?
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 ∩ barC)`
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)
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
If the letters of the word ASSASSINATION are arranged at random. Find the probability that all A’s are not coming together
Without repetition of the numbers, four-digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is ______.
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together 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?
