SAT Math XVII

To figure out probability, you need to work with fractions; the total number of possible outcomes goes on the bottom, ad the number of desired outcomes goes on the top. To figure out the probability of selecting three blue hammers, you need to figure out the probability of getting a blue hammer each time a hammer is selected.

The first time, there are a total of $20$ hammers and 10 of them are blue, so the probability of getting a blue hammer is $\frac{10}{20}=\frac{1}{2}$ .

When the second hammer is selected, there are only $19$ hammers left, and only $9$ of them are blue. So the probability of getting a blue hammer the second time is $\frac{9}{19}$ .

When the third hammer is selected, there are a total of $18$ hammers left and $8$ are blue, so the probability of getting a blue hammer on the third try is $\frac{8}{18}=\frac{4}{9}$ .

To find the probability of selecting three blue hammers, you need to multiply the three separate probabilities:

$\frac{1}{2} \times \frac{9}{19} \times \frac{4}{9} = \boxed{\frac{2}{19}}$ .

---

---

Solution credit: The Princeton Review

this is a dependent type of probability where: P = 10/20 x 9/19 x 8/18 = 2/19