Question

12
8. An integer is chosen randomly from the numbers 1.2,...,25. What is the probability that
the chosen number is divisible by 4 or 5?.: 30rU
25​

Answer 1

Total no. of outcomes, n(S) = 25.

Multiples of 4 among them are 4, 8, 12, 16, 20, 24.

No. of multiples of 4, n(4) = 6.

Multiples of 5 among them are 5, 10, 15, 20, 25.

No. of multiples of 5, n(5) = 5.

When we add up these two, the multiples of 4 as well as 5, i.e., multiples of 20, get added up twice. So we need to deduce it once.

There is only one multiple of 20 among them - 20.

So no. of multiples of 4 and 5, n(4 and 5) = 1

Now, no. of multiples of 4 or 5,

→  n(4 or 5) = n(4) + n(5) - n(4 and 5)

→  n(4 or 5) = 6 + 5 - 1

→  n(4 or 5) = 10

and these 10 numbers are 4, 5, 8, 10, 12, 15, 16, 20, 24, 25.

Hence the probability that the chosen number is either a multiple of 4 or 5, P(4 or 5) = 10/25 = 2/5.