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 8 orders, what is the probability that at least 3 of them will be picked up by the customers?

Answer 1

for binomial distribution:

$P(x=k)=C^k_np^k(1-p)^{n-k}$

we have:

$p=0.6,n=8$

then:

$P(x\ge3)=1-P(x=0)-P(x=1)-P(x=2)$

$P(x=0)=0.0007$

$P(x=1)=0.0079$

$P(x=2)=0.0413$

$P(x\ge3)=1-0.0007-0.0079-0.0413=0.9501$