Twentyfour subjects volunteer fro a study of a new cold medi

Twenty-four subjects volunteer fro a study of a new cold medicine. Eleven of the volunteers are ages 20-39, 8 are ages 40-59, and 5 are age 60 and older. If 9 volunteers are selected at andom, find the following probabilities:

(a) The probability that all volunteers selected are ages 20-39. ___?

(b)The probability that all volunteers selected are ages 20-39 and 3 are age 60 and older. ___?

(c) The probability that 3 of the voluntees are ages 40-59. ___?

Solution

Volunteers for new cold medicine = 24

Total no of ways selecting 9 volunteers from 24 = 24C9 =1307504

a) The probability that all volunteers selected are ages 20-39

= no of ways of selecting all 9 from 11/total ways

= 11C9/1307504

=55/1307504

= 4.2065x10^-5

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b) The probability that all volunteers selected are ages 20-39 and 3 are age 60 and older.

= 11C6(5C3)/20C9

= 462(10)/1307504

=0.003533

c) The probability that 3 of the voluntees are ages 40-59.

= 8C3(16C6)/1307504

= (56)8008/1307504

=0.3493