Question

From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24 is
(a) 6/25
(b) 1/4
(c) 1/6
(d) 2/5

Answer 1

Number divisible by 6 between 1 to 100 = 16
Number divisible by 8 between 1 to 100 = 12
Number divisible by 6 and 8 between 1 to 100 = 4
Number divisible by 24 between 1 to 100 = 4

P(number divisible by 6 or 8) = P(number divisible by 6) + P(number divisible by 8) $-$ P(number divisible by 6 and 8)

$$\begin{gathered} =\frac{16}{100}+\frac{12}{100}-\frac{4}{100} \\ =\frac{24}{100} \\ =\frac{6}{25} \end{gathered}$$


P(number divisible by 6 or 8 but not by 24) = P(number divisible by 6 or 8) $-$ P(number divisible by 24)

$$\begin{gathered} =\frac{6}{25}-\frac{4}{100} \\ =\frac{6}{25}-\frac{1}{25} \\ =\frac{5}{25} \\ =\frac{1}{5} \end{gathered}$$

Disclaimer: None of the given options is correct.