Consider the class level distribution at a small university Discuss and evaluate the probability of the following events: P(M) P(M or Fr) P(M and Fr) P(M | Fr)
Answer and Explanation:
The discussion and evaluation of the probability is shown below:-
The Total number of students in universities is
= 100 + 150 + 130 + 200 + 105 + 103 + 156 + 188
= 1132
The P(m) is
[tex]P(m) = \frac{Total\ number\ of\ male}{Total\ number\ of\ students}[/tex]
[tex]= \frac{530}{1132}[/tex]
= 0.5132
The P(M or Fr) is
P(m or Fr) = P(m) + P(fr) - P(m and fr)
[tex]= 0.5123 + \frac{100+105}{1132} - \frac{100}{1132}[/tex]
= 0.5123 + 0.1810 - 0.0890
= 0.6043
The P(M and Fr) is
[tex]P(M and Fr) = \frac{Number\ of\ male\ freshman}{Total\ number\ of\ student}[/tex]
[tex]= \frac{100}{1132}[/tex]
= 0.0890
The P(M | Fr) is
[tex]P(M | Fr) = \frac{P(M and Fr)}{P(Fr)}[/tex]
[tex]= \frac{0.0890}{0.1810}[/tex]
= 0.4917