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Sample Question 13:
Step 1: Note the three unique digits \(1\), \(3\), and \(5\) form six different three-digit numbers: \(135\), \(153\), \(351\), \(315\), \(513\), \(531\).
Step 2: A number is divisible by 5 only if it ends with a 5. From our list of three-digit numbers, only two numbers (\(135\), \(315\)) end with 5.
Step 3: Compute the probability by dividing the number of favorable outcomes (numbers ending with 5) by the total number of outcomes (all possible three-digit numbers). Therefore, the probability is \(\frac{2}{6} = \frac{1}{3}\).
The answer is \(\frac{1}{3}\) or choice \(\textbf{(B)}\).
A three-digit integer contains one of each of the digits \(1\), \(3\), and \(5\). What is the probability that the integer is divisible by \(5\)?
\(\textbf{(A)}\ \frac{1}{6}\qquad\textbf{(B)}\ \frac{1}{3}\qquad\textbf{(C)}\ \frac{1}{2}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{5}{6}\)
Answer Keys
Question 13: BSolutions
Question 13Step 1: Note the three unique digits \(1\), \(3\), and \(5\) form six different three-digit numbers: \(135\), \(153\), \(351\), \(315\), \(513\), \(531\).
Step 2: A number is divisible by 5 only if it ends with a 5. From our list of three-digit numbers, only two numbers (\(135\), \(315\)) end with 5.
Step 3: Compute the probability by dividing the number of favorable outcomes (numbers ending with 5) by the total number of outcomes (all possible three-digit numbers). Therefore, the probability is \(\frac{2}{6} = \frac{1}{3}\).
The answer is \(\frac{1}{3}\) or choice \(\textbf{(B)}\).