# Math Help - Probability Question

1. ## Probability Question

Question:

You have 40 different books (20 math, 15 history and 5 geography)

A. You pick on book at random. What is the probability that the book is a history book?

B. You pick two books at random, one at at time. What is the probability that both books are history books?

2. Originally Posted by oldguy
You have 40 different books (20 math, 15 history and 5 geography)
A. You pick on book at random. What is the probability that the book is a history book?
B. You pick two books at random, one at at time. What is the probability that both books are history books?
Tell us what you think the answers are.
${40} \choose 2$ ways to pick two book.

3. My initial throught was 15/40 or 5/9 for part A.

4. Originally Posted by oldguy
Question:

You have 40 different books (20 math, 15 history and 5 geography)

A. You pick on book at random. What is the probability that the book is a history book?

B. You pick two books at random, one at at time. What is the probability that both books are history books?
Part B is ambiguous, is the first book replaced before the second is chosen?

RonL

5. No. A and B are two seperate events.

6. From the wording I assume that the two books are taken without replacement.
$\frac{{\left( {\begin{array}{c}
{15} \\
2 \\
\end{array}} \right)}}{{\left( {\begin{array}{c}
{40} \\
2 \\
\end{array}} \right)}} = \frac{{15 \cdot 14}}{{40 \cdot 39}}
$