Question

There are two types of residential properties in Pittsburg. These types are independent. Andi finds that houses account for 35% of residential properties in Pittsburgh and 65% account for apartments. If she randomly picks 20 residential properties in Pittsburg. What is the probability that fewer than 10 of these properties are houses?

Answer 1

Here, n = 20, p = 0.35, (1 - p) = 0.65 and x = 10
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X < 10).
P(X < 10) = (20C0 * 0.35^0 * 0.65^20) + (20C1 * 0.35^1 * 0.65^19) + (20C2 * 0.35^2 * 0.65^18) + (20C3 * 0.35^3 * 0.65^17) + (20C4 * 0.35^4 * 0.65^16) + (20C5 * 0.35^5 * 0.65^15) + (20C6 * 0.35^6 * 0.65^14) + (20C7 * 0.35^7 * 0.65^13) + (20C8 * 0.35^8 * 0.65^12) + (20C9 * 0.35^9 * 0.65^11)

P(X < 10) = 0.0002 + 0.002 + 0.01 + 0.0323 + 0.0738 + 0.1272 + 0.1712 + 0.1844 + 0.1614 + 0.1158

P(X < 10) = 0.8783