Question

there are 5 blue pencils and 3 gold pencils in a container. if 2 pencils are drawn at random without replacement, what is the probability that both pencils drawn are gold? express your answer as a fraction in simplest form.

Answer 1

\[\frac{3}{8}\times \frac{2}{7}\]

Answer 2

without replacement tells you the draws are independent
that allows you to use P(A and B) = P(A)P(B)

where A is the probability that the first draw is a gold pencil
and B the prob. that the second draw is a gold pencil

Answer 3

actually without replacement tells you the draws are DEPENDENT

Answer 4

so it is \(P(A\cap B)=P(A|B)P(B)\)