Discussion
Cards bearing numbers 12, 13, 14, ... , 70, 71 (one number on one card) are kept in a box and then a card is drawn from the box without looking into it. What is the probability that the card drawn has the number which is not a prime ?
Answer: D
The probability is \(\frac{3}{4}\).
The cards run from 12 to 71, so there are 71 - 12 + 1 = 60 cards. The primes among them are 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 and 71, which is 15 numbers.
\[ \begin{aligned} P(\text{not prime}) &= \frac{60 - 15}{60} \\ &= \frac{45}{60} = \frac{3}{4} \end{aligned} \]
The options with denominator 59 miscount the cards (forgetting to include both ends), and \(\frac{1}{4}\) is the probability of drawing a prime.
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