Question

Suppose that there is a 63 percent chance of randomly selecting a ripe avocado. If you are picking avocados from the bin, you keep inspecting avocados and stop upon finding a ripe avocado.What is the probability that you inspect inclusively between 5 and 6 avocados from the bin?

Answer 1

We are given that:

P(selecting a ripe avocado), say p = 63% = 0.63

=> P(not selecting a ripe avocado) = 1 - p = 1 - 0.63 = 0.37

Now, we are given that we are picking avocados from the bin and that we stop when we find a ripe avocado.

Let X denote the number of avocados we pick from the bin.

Now, we could find a ripe avocado on the first attempt, second attempt, third attempt and so on. Thus, the possible values of X (or the support of X) is {1,2,3,...}.

Now, we find the probability mass function of X:

Now, the probability that we inspect inclusively between 5 and 6 avocados from the bin is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.