Question

Set M consists of all the integers from $-15$ to $15$, inclusive. If a number is drawn at random from set M, then what is the probability that the number is a multiple of $3$?

• A. $\frac{11}{31}$
• B. $\frac{9}{31}$
• C. $\frac{5}{10}$
• D. $\frac{4}{5}$
• E. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{11}{31}$

Probability questions on the SAT are often just counting problems in disguise. To determine probability, we need to count the number of ways a desired event can happen and then divide by the total number of ways the event can happen (whether desired or not).
For this question, we first need to count the numbers of ways we can draw a multiple of $3$ from the set M. The possibilities are: $15,12,9,6,3,0,3,6,9,12$, and $15$; so there are $11$ multiples. The total number of integers in set M is $31$, so the answer is $11/31$.