In a large national population of college students, 61% attend 4-year institutio

Question

In a large national population of college students, 61% attend 4-year institutions and the rest attend 2-year institutions. Males make up 44% of the students in the 4-year institutions and 41% of the students in the 2-year institutions. Find the four probabilities for each combination of gender and type of institution in the following table. Be sure that your probabilities sum to 1. Let M = male and C = attends a 4-year institution, Consider randomly selecting a female student from this population. What is the probability that she attends a 4-year institution? Give your answer to 2 decimal places. Fill in the blank: P(C|M) = _____.

Explanation / Answer

here P(C)=0.61

and P(Cc)=1-0.61=0.39

and P(M|C)=0.44

hence P(MnC)=P(C)*P(M|C) =0.61*0.44=0.2684

threfore P(McnC) =0.61-0.2684=0.3416

similarly P(M|Cc)=0.41

hence P(MnCc)=0.41*0.39=0.1599

P(McnCc)=0.39-0.1599=0.2301

therefore below is table

from above P(C|Mc)=0.3416/0.5717=0.60

male female total 4 year 0.2684 0.3416 0.61 2 year 0.1599 0.2301 0.39 total 0.4283 0.5717 1

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