Question

One number is selected at random from the first 100 natural numbers. Find the probability that this number is divisible by 7.

Answer 1

Here, U = {1, 2, 3, …, 100}

One number is selected at random.

∴ Total number of primary outcomes

n = ¹⁰⁰C₁ = 100A = Event that the number selected is divisible by 7.

A = {7, 14, 21, 28, …, 91, 98}

∴ Favourable outcomes for the event A is m = 14.

Hence, P(A) = \(\frac{m}{n} = \frac{14}{100} = \frac{7}{50}\)