The random variable X represents the number of successes in 10 independent Bernoulli trials - HSC - SSCE Mathematics Extension 1 - Question 6 - 2021 - Paper 1

To find the value of r, we need to calculate the probability of getting at least one success in 10 trials.

First, we can calculate the probability of getting zero successes:

$P(X = 0) = (1 - p)^{n} = (1 - 0.9)^{10} = 0.1^{10} = 10^{-10}$

Consequently, the probability of getting at least one success is:

$P(X ≥ 1) = 1 - P(X = 0) = 1 - 10^{-10}$

Since $10^{-10}$ is a very small number, we can conclude that $P(X ≥ 1)$ is virtually equal to 1, implying that r is very close to 1.