# SAT Math Multiple Choice Practice Question 479: Answer and Explanation

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**Question: 479**

**20.** A bag contains 4 red hammers, 10 blue hammers, and 6 yellow hammers. If three hammers are removed from the bag at random and no hammer is returned to the bag after removal, what is the probability that all three hammers will be blue?

A.

B.

C.

D.

E.

**Correct Answer:** D

**Explanation:**

**D** To figure out probability, you need to work with fractions; the total number of possible outcomes goes on the bottom, and 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 . 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 . 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 . To find the probability of selecting three blue hammers, you need to multiply the three separate probabilities: . By the way, A and C are Joe Bloggs answers because he doesn't consider how the probability changes with each event.