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
you really need to draw a Venn diagram.
Pr(Senior!Female)= 450/1800
Pr(Female!Senior)=450/800
To answer these questions, we can use conditional probability, which is a measure of the probability of an event occurring given that another event has already occurred.
1. Probability that a student selected at random is a senior given that the selected student is female:
To find this probability, we need to determine the number of females who are seniors and divide it by the total number of females.
Number of females who are seniors: 450
Total number of females: 1800
Therefore, the probability that a student selected at random is a senior given that the selected student is female is:
P(Senior | Female) = Number of females who are seniors / Total number of females
P(Senior | Female) = 450 / 1800 = 0.25 or 25%
2. Probability that a student selected at random is female given that the selected student is senior:
To find this probability, we need to determine the number of seniors who are female and divide it by the total number of seniors.
Number of seniors who are female: 450
Total number of seniors: 800
Therefore, the probability that a student selected at random is female given that the selected student is a senior is:
P(Female | Senior) = Number of seniors who are female / Total number of seniors
P(Female | Senior) = 450 / 800 = 0.5625 or 56.25%