Advertisements
Advertisements
प्रश्न
In a lottery, a person chooses six different numbers at random from 1 to 20, and if these six numbers match with six number already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?
Advertisements
उत्तर
Total number of ways in which one can choose six different numbers from 1 to 20 = 20C6
∴ Total number of elementary events = 20C6 = 38760
Hence, there are 38760 combinations of 6 numbers.
Out of these combinations, one is already fixed by the lottery committee.
Favourable number of elementary events = 1
∴ Required probability = \[\frac{1}{38760}\]
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 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 is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up.
From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.
Check whether the following probabilities P(A) and P(B) are consistently defined
P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
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) |
| `1/3` | `1/5` | `1/15` | .... |
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.35 | ... | 0.25 | 0.6 |
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?
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 and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.
A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?
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 |
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that: all 10 are defective
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that all 10 are good
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
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(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 `P(A ∩ barB)`
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 no two A’s are coming together
In a non-leap year, the probability of having 53 tuesdays or 53 wednesdays is ______.
Three numbers are chosen from 1 to 20. Find the probability that they are not consecutive ______.
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 ______.
A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is ______.
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
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
