Question

You apply for a summer internship with a startup company, and your chance of getting an offer

is 80% if you well prepare for an interview. Otherwise, you will only get 20% chance for an

offer. Suppose that the likelihood of your preparation going well is 30%. What is the probability

that you get the internship?

Answer 1

Answer :

Here we have given the probabilities. So first we define the events as

A = Event that you are well prepare for the interview.

It's complementary event is given by

A' = Event that you are not well prepare for the interview.

B = Event that getting an internship offer.

Now let's summaries the given probabilities of the given events as

P ( A ) = 0.30 And

P ( A ' ) = 1 - P ( A ) = 1 - 0.30 = 0.70

P ( B / A ) = 0.80 And

P ( B / A' ) = 0.20

Here we want to find the ' Probability that you get the internship offer.'

That is the probability of the event B, that is P ( B ) = ?

Here the given events are dependent and the event A forms an partition. So to find the probability of the event B we need to use the " Theorem of total probability". Which is given by

  

Now let's plug the values in the formula as

P ( B ) = 0.80 * 0.30 + 0.20 * 0.70 = 0.24 +0.14 = 0.38

Therefore P ( B ) = 0.38

Then the required probability of getting the internship is 0.38.