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In: Statistics and Probability
A small international agency in Amsterdam employs 30 people, of whom 3 are Russian, 5 are...
A small international agency in Amsterdam employs 30 people, of whom 3 are Russian, 5 are Dutch, 4 are British, 6 are French, 5 are German, 3 are Italian, and 4 are Polish. If 7 of these employees are chosen at random, what is the expected number of nationalities in that group?
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ANSWER::
Solution-:
We given the number Russian as 1, Dutch as 2, British as 3, French as 4, German as 5, Italian as 6, Polish as7
Total employs = 30,
suppose x takes value 1,2,3,4,5,6,7 and we find corresponding probabilities in following table:
| X | P(x) | x*P(x) |
| 1 | 3/30=0.1000 | 0.1000 |
| 2 | 5/30=0.1667 | 0.3333 |
| 3 | 4/30=0.1333 | 0.4000 |
| 4 | 6/30=0.2000 | 0.8000 |
| 5 | 5/30=0.1667 | 0.8333 |
| 6 | 3/300.1000 | 0.6000 |
| 7 | 4/30=0.1333 | 0.9333 |
| Total | 1.00 | 4 |
Therefore, the expected number of nationalities in that group is,
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