[spoiler]9/32 or 1/24 depending on assumptions made
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[spoiler]i don't think this real GMAT q.
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there can be 4 single digit multiples of 3 ==> 0,3,6,9
and there are 8 primes numbers less than 20 ==> 2,3,5,7,11,13,17,19

counting two sets will give 4*8 or 32 combination sets
8 by 0
1 by 9 ==> 9 good selections

9/32 is my answer if we count for 0 as a multiple of 3 as well

if we don't count 0 as a multiple of 3, as 0 is the multiple of all numbers then
we have 3 single digit multiples of 3 and 8 primes
this should give us counting of 24 possibilities with 1 good selection
and i would answer then 1/24

jayanti wrote:if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20. what is the probability that this product will be a multiple of 45

it is 1/24, my approach was to choose 1 no from the 8 digit i.e 1/8 and 1 no from 3 nos which are multiples of 3 i.e: 1/3 then multiplied both of them 1/8 * 1/3= 1/24.

Is it right???

it's the same, you've combined two probabilities here
the important condition for combining two or several probabilities is that the events are not mutually exclusive and independent

jayanti wrote:it is 1/24, my approach was to choose 1 no from the 8 digit i.e 1/8 and 1 no from 3 nos which are multiples of 3 i.e: 1/3 then multiplied both of them 1/8 * 1/3= 1/24.

Is it right???