Question

An ice cream store reports that 30% of the cones they sell are "jumbo" size. You want to see what a "jumbo" cone looks like before you decide to purchase one, so you stand and watch the sales for awhile. What is the (geometric) probability that the first "jumbo" cone you see them sell is the 4th cone

Answer 1

Answer:

0.1029 is the probability that the first "jumbo" cone sold is the $4^{th}$ cone.

Step-by-step explanation:

We are given the following information:

We treat a jumbo cone as a success.

P(Jumbo cone) = 30% = 0.3

Then the number of cones follows a geometric distribution, where

$P(X=x) = p(1-p)^{x-1}$

where $(x-1)$ is the number of failures before the first success, p is the probability of success.

Now, we are given x = 4

We have to evaluate:

$P(x = 4) = (0.3)(1-0.3)^{4-1}\\P(x =4) = (0.3)(1-0.3)^{3}\\P(x =4) =0.1029$

0.1029 is the probability that the first "jumbo" cone sold is the $4^{th}$ cone.