Answer:
[tex]\bold{\dfrac{63}{143}}[/tex]
Step-by-step explanation:
Number of Democrats = 6
Number of Republicans = 7
Total number of members = 6+7 = 13
To find:
Probability of selecting two Democrats and two Republicans if 4 members are selected in the committee = ?
Solution:
This is a selection problem.
Total number of ways to select 4 members in the committee out of total 13 = [tex]_{13}C_4 = \dfrac{13\times 12\times 11\times 10}{4\times 3\times 2} = 715[/tex]
Number of ways to select 2 Democrats = [tex]_{6}C_2 = \dfrac{6\times 5}{2} = 15[/tex]
Number of ways to select 2 Republicans = [tex]_{7}C_2 = \dfrac{7\times 6}{2} = 21[/tex]
Number of ways to select 2 Democrats and 2 Republicans = 15 [tex]\times[/tex] 21 = 315
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, required probability:
[tex]\dfrac{315}{715} = \bold{\dfrac{63}{143}}[/tex]
