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प्रश्न
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?
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उत्तर
Let A represent selection of male and B represent person's age above 35 years.
Total number of males = 3
Total person above 35 years of age = 2
There is 1 male above 35 years of age.
Total persons are 5. Ways to select one of them = `""^5C_1 = 5`
Ways to select 1 man from 3 men = `""^3C_1 = 3`
∴ P(A) = `(""^3C_1)/(""^5C_1) = 3/5`
Ways to select one person above 35 years = `""^2C_1 = 2`
P(B) = `(""^2C_1)/(""^5C_1) = 2/5`
P(A ∩ B) = `(""^2C_1)/(""^5C_1) = 1/5`
P(A ∪ B) = P(male or person above 35 years)
= P(A) + P(B) − P(A ∩ B)
= `3/5 + 2/5 - 1/5`
= `4/5`
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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` |
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| `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 |
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| (iv) |
\[\frac{1}{14}\]
|
\[\frac{2}{14}\]
|
\[\frac{3}{14}\]
|
\[\frac{4}{14}\]
|
\[\frac{5}{14}\]
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\[\frac{6}{14}\]
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\[\frac{15}{14}\]
|
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