Question

48 can be written as the product of two different numbers a and b such as 48 = a*b. What is the probability that a is 3.

Answer 1

First we've to find the no. of factors of 48.

48 = 2⁴ × 3

No. of factors can be found by adding each exponents of the prime numbers in the prime factorization by 1, and then by multiplying.

∴ No. of factors = (4 + 1)(1 + 1) = 5 × 2 = 10

So we can write 48 as a × b in 10 different ways.

(Remember that 3 × 16 and 16 × 3 are of different ways because it's a = 3 and b = 16 in the first one and a = 16 and b = 3 in the second one. So there's not 5 different ways only.)

So the no. of total outcomes is 10.

Among these, there is only 1 possible outcome in which a = 3.

48 = 3 × 16.

∴ No. of favourable outcome = 1

∴ Probability = 1/10

Thank you. Have a nice day. :-))

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