Discussion
Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
Answer: A
Count each set, then remove the overlap.
\[ \text{multiples of 4} = \left\lfloor \tfrac{50}{4} \right\rfloor = 12, \qquad \text{multiples of 7} = \left\lfloor \tfrac{50}{7} \right\rfloor = 7 \]
\[ \text{multiples of 28} = \left\lfloor \tfrac{50}{28} \right\rfloor = 1 \]
\[ 12 + 7 - 1 = 18 \quad\Longrightarrow\quad P = \frac{18}{50} = \frac{9}{25} \]
28 is the only number counted twice, being a multiple of both 4 and 7.
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