Advertisements
Advertisements
Question
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability thatat least one is defective
Advertisements
Solution
Out of 100 bulbs, 10 can be chosen in 100C10 ways.
So, total number of elementary events = 100C10
Probability for at least one defective bulb = 1 – Probability (all 10 are non-defective)
= \[1 - \frac{^{80}{}{C}_{10}}{^{100}{}{C}_{10}}\]
APPEARS IN
RELATED QUESTIONS
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 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) = 0.4, 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 |
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that all will be blue?
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?
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.
Two unbiased dice are thrown. Find the probability that the sum of the numbers obtained on the two dice is neither a multiple of 2 nor a multiple of 3
A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that all the balls are of different colours.
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?
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
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 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
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
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 ∪ B)
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
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
Seven persons are to be seated in a row. The probability that two particular persons sit next to each other 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 probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11.
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 |
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?
