Question

In a random sample of 600 smart phines used in Spain, 429 had the android system,107 had window operating system, and the rest had Apple system.
What is the probability the first two have Apple operating system and the third has Window OS?

Answer 1

Let's estimate the probability of each operating system:

$$P(android) = \frac{429}{600} = \frac{143}{200}$$ $$P(windows) = \frac{107}{600}$$ $$P(Apple) = \frac{600 - 429 - 107}{600} = \frac{64}{600} = \frac{8}{75}$$

Thus if we have 3 people, then probability that first two have Apple and third has Windows OS equals to

$$P(android)^2 P(windows) = \left(\frac{143}{200}\right)^2 \cdot \left(\frac{8}{75}\right) = \frac{20449}{375000}$$