2005 CEMC Pascal Problems/Problem 4

Problem

Six balls, numbered $2, 3, 4, 5, 6, 7,$ are placed in a hat. Each ball is equally likely to be chosen. If one ball is chosen, what is the probability that the number on the selected ball is a prime number?

$\text{ (A) }\ \frac{1}{6} \qquad\text{ (B) }\ \frac{1}{3} \qquad\text{ (C) }\ \frac{1}{2} \qquad\text{ (D) }\ \frac{2}{3} \qquad\text{ (E) }\ \frac{5}{6}$

Solution

To find the probability of the ball having a prime number, we can find the number of ways that we can select a ball with a prime number divided by the number of balls.

From the list, the prime numbers are $2, 3, 5$ and $7$ . This gives us $4$ ways to select a ball with a prime number on it.

Dividing this by the number of balls, we have;

$\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \boxed {\textbf {(D) } frac{2}{3}}$

~anabel.disher

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2005 CEMC Pascal Problems/Problem 4

Problem

Solution