Question

Two numbers 'a' and 'b' are selected, successively without replacement in that order, from integers 1 to 10. The probability that a/b is an integer, is ________.

Answer 1

Total number of outcomes = Number of selections of two numbers 'a' and 'b' successively without replacement = 10 × 9 = 90

Let E be the event that a/b is an integer. The outcomes in favour of event E are (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1), (9, 1), (10, 1), (4, 2), (6, 2), (8, 2), (10, 2), (6, 3), (9, 3), (8, 4) and (10, 5).

Favourable number of outcomes = 17

∴ Probability that a/b is an integer = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{17}{90}$

Two numbers 'a' and 'b' are selected, successively without replacement in that order, from integers 1 to 10. The probability that a/b is an integer, is $\underline{\frac{17}{90}}$.