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 

Options

• 6/25

• 1/4

•  1/6

•  2/5

• None of these

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)

\[= \frac{16}{100} + \frac{12}{100} - \frac{4}{100}\]

\[ = \frac{24}{100}\]

\[ = \frac{6}{25}\]

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

\[= \frac{6}{25} - \frac{4}{100}\]

\[ = \frac{6}{25} - \frac{1}{25}\]

\[ = \frac{5}{25}\]

\[ = \frac{1}{5}\]