A town council has 13 members, 7 Democrats and 6 Republicans.

Question

Membership selection. A town council has 13 members, 7 Democrats and 6 Republicans.

 

(A) If the president and vice-president are selected at random, what is the probability that they are both Democrats?

(B) If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?

Answer 1

(A) (7/13)(6/12)=0.269

 

There is a 26.9% chance, if the president and vice-president are selected at random, that they are both Democrats.

 

(B) (6/13)(5/12)(7/11)=0.122

 

There is a 12.2% chance, if a 3-person committee is selected at random, that Republicans make up the majority.