In: Statistics and Probability
(a)
Population:
Footballers who used drugs = 4
Footballers who did not use drugs = 18
Total footballers = 22
Sample:
Footballers who used drugs = 1
Footballers who did not use drugs = 4
Total footballers = 5
Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334
Number of ways of selecting 1 Footballer who used drugs from 4 Footballers who used drugs = 4C1 = 4
Number of ways of selecting 4 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C4 = 3060
So,
the probability that :one of the 4 footballers who have used drugs will be included in the tests = (4 X 3060)/26334 = 0.4648
So,
Answer is:
0.4648
(b)
Population:
Footballers who used drugs = 4
Footballers who did not use drugs = 18
Total footballers = 22
Sample:
Footballers who used drugs = 2
Footballers who did not use drugs = 3
Total footballers = 5
Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334
Number of ways of selecting 2 Footballer who used drugs from 4 Footballers who used drugs = 4C2 = 6
Number of ways of selecting 3 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C3 = 816
So,
the probability that :two of the 4 footballers who have used drugs will be included in the tests = (6 X 816)/26334 = 0.1859
So,
Answer is:
0.1859
(c)
Population:
Footballers who used drugs = 4
Footballers who did not use drugs = 18
Total footballers = 22
Sample:
Footballers who used drugs = 3
Footballers who did not use drugs = 2
Total footballers = 5
Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334
Number of ways of selecting 3 Footballer who used drugs from 4 Footballers who used drugs = 4C3 = 4
Number of ways of selecting 2 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C2 = 153
So,
the probability that :three of the 4 footballers who have used drugs will be included in the tests = (4 X 153)/26334 = 0.0232
So,
Answer is:
0.0232
(d)
Population:
Footballers who used drugs = 4
Footballers who did not use drugs = 18
Total footballers = 22
Sample:
Footballers who used drugs = 4
Footballers who did not use drugs = 1
Total footballers = 5
Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334
Number of ways of selecting 4 Footballer who used drugs from 4 Footballers who used drugs = 4C4 = 1
Number of ways of selecting 1 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C1 = 18
So,
the probability that :four of the 4 footballers who have used drugs will be included in the tests = (1 X 18)/26334 = 0.0007
So,
Answer is:
0.0007