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प्रश्न
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
पर्याय
6/25
1/4
1/6
2/5
None of these
उत्तर
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)
\[= \frac{6}{25} - \frac{4}{100}\]
\[ = \frac{6}{25} - \frac{1}{25}\]
\[ = \frac{5}{25}\]
\[ = \frac{1}{5}\]
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