How many females participated in the academic competition? How many of them are freshmen?
1/4
Practice makes perfect
The probability that an event will occur, given that another event has already occurred, is called a conditional probability. Since we want to know the conditional probability of selecting a freshman student given that she is a female, let's highlight the number of female freshmen and the total number of females in the given two-way frequency table.
Male
Female
Totals
Freshmen
3
5
8
Sophomores
6
4
10
Juniors
7
5
12
Seniors
4
6
10
Totals
20
20
40
The condition that the student selected is a female limits the total outcomes to the 20 females. Of those 20 students, 5 are freshmen.
P(Freshman | Female)&=Female freshmen/Female [1em]
P(Freshman | Female)&=5/20=1/4
