Answer to Question #121905 in Statistics and Probability for rishabh parihar

Question

The following is a breakdown of faculty members at IIM-A.
Rank No of males No of females
Professor 20 12
Associate Prof 18 20
Asst Prof 25 30.
What is the probability that a faculty member selected at random is
a) Female.
b) A female professor
c) A female or professor.
d)A professor or asst. Prof

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} & Male & Female & Total \\ \hline Professor & 20 & 12 & 32 \\ \hdashline Associate\ Prof & 18 & 20 & 38 \\ \hdashline Assistant \ Prof & 25 & 30 & 55 \\ \hdashline Total & 63 & 62 &125 \end{array}$$

a)

$$P(F)={62\over 125}=0.496$$

b)

$$P(F\cap Prof)={12\over 125}=0.096$$

c)

$$P(F\cup Prof)=P(F)+P(Prof)-P(F\cap Prof)=$$

$$={62\over 125}+{32\over 125}-{12\over 125}={82\over 125}=0.656$$

d)

$$P(Prof\cup Assist\ Prof)=P(F)+P(Assist \ Prof)=$$

$$={32\over 125}+{55\over 125}={87\over 125}=0.696$$