Answer to Question #264119 in Statistics and Probability for Nathan

Question

Takealot orders in a certain area can either be delivered by Takealot or picked up by the customer at a pick-up point. Historically, 40% of the orders are delivered by Takealot. Given 12 orders made within a certain hour, what is the probability that at least 3 of them will be picked up by the customers?

Answer 1

Let X be the number of orders picked up by the customers. Then X ~ Bin(n, p), where n = 12, p = 1-0.4 = 0.6. X ~ Bin(12, 0.6), then $P(X=k)={12 \choose k}*0.6^k*0.4^{12-k}$

$P(X≥3) = 1-P(X<3)=1-P(X=2)-P(X=1)-P(X=0)=1-0.0025-0.0003-0.000=0.9972$