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प्रश्न
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
उत्तर
Given that: Number of red balls = 8
Number of white balls = 5
P(all the three balls are red) = `(""^8C_3)/(""^13C_3)`
= `((81)/(3!5!))/((131)/(3!10!))`
= `(8!)/(3!5!) xx (3!10!)/(13!)`
= `(8 xx 7 xx 6 xx 51)/(5!) xx (10!)/(13 xx 12 xx 11 xx 10!)`
= `(8 xx 7 xx 6)/(13 xx 12 xx 11)`
= `28/143`
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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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