The composition of the enate of the 107th COngress is 51 Republicans, 48 Democra
ID: 3325888 • Letter: T
Question
The composition of the enate of the 107th COngress is 51 Republicans, 48 Democrates, and 1 Indepenent. A new committee is being formed to study ways to benefit the arts in education. If 3 Senators are selected at random to head the committee, find the probability of the following.
Enter the answers as fractions or as decimals rounded to 3 decimal places
a) The group of 3 consist of all Republicans
b) The group of 3 consist of all Democrats
c ) The group of 3 consists of 1 from each party, including the Inepenent
Explanation / Answer
Solution:
Total number of competitors = 100
Total number of republicans = 51
Total number of Democrats = 48
Total number of independent = 1
( a )
Probability of selecting group of 3 consist of all Republicans = 51c3 / 100c3 = 20825 / 161700
= 0.1288
( b )
Probability of selecting group of 3 consist of all Democrats = 48c3 / 100c3 = 17296 / 161700
= 0.1070
( c )
Probability of selecting group of 3 consists of 1 from each party, including the Inepenent = 51 * 48 * 1 / 100c3
= 2448 / 161700
= 0.0151
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