Blue Nile University recently conducted a survey of undergraduate students in order to gather information about the usage of the library. The population for this study included all 4000 undergraduate students enrolled in the university. The library officers are interested in increasing usage, particularly among females (F) and seniors (S) at the university. Of the 4000 students, 800 students are seniors, 1800 students are females and 450 of the 1800 females are seniors. Required:

Question

Blue Nile University recently conducted a survey of undergraduate students in order to gather information about the usage of the library. The population for this study included all 4000 undergraduate students enrolled in the university. The library officers are interested in increasing usage, particularly among females (F) and seniors (S) at the university. Of the 4000 students, 800 students are seniors, 1800 students are females and 450 of the 1800 females are seniors. Required:

What is the probability that a student selected at random is a senior given that the selected student is female?
What is the probability that a student selected at random is female given that the selected student is senior?

Answer 1

i need answer

Answer 2

To find the probability that a student selected at random is a senior given that the selected student is female, we can use the formula for conditional probability:

P(Senior | Female) = P(Senior and Female) / P(Female)

We are given that there are 4000 undergraduate students in total, and 1800 of them are females. This gives us the probability of selecting a female student:

P(Female) = 1800 / 4000 = 0.45

We are also given that out of the 1800 females, 450 of them are seniors. This gives us the probability of selecting a senior and female student:

P(Senior and Female) = 450 / 4000 = 0.1125

Plugging these values into the formula, we get:

P(Senior | Female) = 0.1125 / 0.45 = 0.25

So the probability that a student selected at random is a senior, given that the selected student is female, is 0.25.

To find the probability that a student selected at random is female, given that the selected student is a senior, we can use the same formula:

P(Female | Senior) = P(Female and Senior) / P(Senior)

We are given that there are 800 senior students out of the total 4000 students, so the probability of selecting a senior student is:

P(Senior) = 800 / 4000 = 0.2

We are also given that out of the 450 senior students, 1800 of them are females. This gives us the probability of selecting a female and senior student:

P(Female and Senior) = 450 / 4000 = 0.1125

Plugging these values into the formula, we get:

P(Female | Senior) = 0.1125 / 0.2 = 0.5625

So the probability that a student selected at random is female, given that the selected student is a senior, is 0.5625.