The science club has five female and five male students. the club will randomly select two people to compete in the upcoming science competition. what is the probability that both people chosen are females?

To determine the probability that both people chosen are females, we will use the rule of multiplication. 
Let event A = the event that the first person chosen is female; and let B = the event that the second person is female. 
To start, it is given that there are 10 students, 5 of them are females.  Therefore, P(A) = 5/10
After the first selection, there are 9 students, 4 of them are females. Therefore, P(A|B) = 4/9
Based on the rule of multiplication:

P(A∩B) = P(A) * P(A|B)
P(A∩B) = (5/10) (4/9)
P(A∩B) = 20/90
P(A∩B) = 2/9

The probability that both people chosen are females is 2/9.