Q.3 (B)(iv) A two digit number is formed using digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is :
(a) an odd number.
(b) a multiple of 5.
Best answer
Answer: (a) \(\dfrac{4}{5}\) (b) \(\dfrac{1}{5}\)
A two digit number is formed from 5 digits without repetition: the tens place can be filled in 5 ways and the units place in 4 ways, so \(n(S) = 5 \times 4 = 20\).
(a) Event A : the number is odd, so the units digit is 3, 5, 7 or 9 (4 ways) and the tens digit can be any of the remaining 4 digits.
\(n(A) = 4 \times 4 = 16\), so \(P(A) = \dfrac{16}{20} = \dfrac{4}{5}\).
(b) Event B : the number is a multiple of 5, so the units digit must be 5 (1 way) and the tens digit can be any of the other 4 digits.
\(n(B) = 1 \times 4 = 4\), so \(P(B) = \dfrac{4}{20} = \dfrac{1}{5}\).
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