Advertisements
Advertisements
प्रश्न
Three-digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
विकल्प
`1/16`
`16/25`
`1/645`
`1/25`
Advertisements
उत्तर
`1/25`
Explanation:
Since a 3-digit number cannot start with digit 0.
The hundredth place can have any of the 4 digits.
Now, the tens and units place can have all the 5 digits.
Therefore, the total possible 3-digit numbers are 4 × 5 × 5
i.e., 100.
The total possible 3 digit numbers having all digits same = 4
Hence, P(3-digit number with same digits) = `4/100 = 1/25`.
APPEARS IN
संबंधित प्रश्न
A die is thrown, find the probability of following events:
- A prime number will appear,
- A number greater than or equal to 3 will appear,
- A number less than or equal to one will appear,
- A number more than 6 will appear,
- A number less than 6 will appear.
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?
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
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?
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.
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
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?
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 |
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) |
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
\[\frac{1}{7}\]
|
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 |
| (iii) | 0.7 | 0.06 | 0.05 | 0.04 | 0.03 | 0.2 | 0.1 |
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 thatat least one 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 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
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.
In a leap year the probability of having 53 Sundays or 53 Mondays is ______.
Three squares of chessboard are selected at random. The probability of getting 2 squares of one colour and other of a different colour 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?
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 C will be selected?
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)`
If the letters of the word ASSASSINATION are arranged at random. Find the probability that two I’s and two N’s come together
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
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 repetition of digits is not allowed?
