A bag contains tickets numbered 11, 12, 13, 14, ..., 30. A ticket is taken out form the bag at random. Find the probability that the number on the drawn ticket is (a) a multiple of 7 (b) greater than 15 and a multiple of 5.

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Solution

Total number of tickets = 20
(i) Out of the given ticket numbers, the multiples of 7 are = 14, 21 and 28
Let E₁ be the event of getting a multiple of 7.
Number of favourable outcomes = 3
∴ P (getting a multiple of 7 ) = $\frac{3}{20}$

(ii) Out of the given ticket numbers, the multiples of 5 are = 15, 20, 25 and 30
Let E₂ be the event of getting a number that is greater than 15 and a multiple of 5.
Then, number of favourable outcomes = 3
∴ P (getting a ticket number that is greater than 15 and a multiple of 5 ) = $\frac{3}{20}$

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