Question

If there are 4 Democrats and 3 Republicans on a committee, what is the probability that a Democrat will be the chair of the committee and a Republican will be the alternate? Assume that the chair and the alternate are chosen randomly. Round the answer to the nearest hundredth So confused it it 2 spots?

Answer 1

and is it a combination?

Answer 2

the probability that a democrat is chair is \(\frac{4}{7}\)
then the probability that a republican is the alternate, given that the chair is a democrat, is \(\frac{3}{6}\) (since one person has already been picked, and it was a demcrat)

then multiply to get your answer
\[\frac{4}{7}\times\frac{1}{2}=\frac{2}{7}\]

Answer 3

if you think of it as picking the alternate first, you get the same answer via
\[\frac{3}{7}\times \frac{4}{6}\]

Answer 4

Got it so I get that that you took 7 to 6 cause a democrat already had it thanks

Answer 5

exactly
you can also compute as
\[\frac{4\times 3}{\binom{7}{2}}\] but that is more complicated to compute

Answer 6

What about this A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?

Answer 7

5/8(3/7)?