Respuesta :
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.
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.
The probability that both people chosen are females in the random selection of two people to complete the project is 2/9.
What is probability?
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
Given information-
The number of females in the science club is 5.
The number of males in the science club is 5.
As club will randomly select two people to compete in the upcoming science competition.
Thus the probability of chosen 1 person as female is find first.
The total females are 5 and total number of person is 10. Thus the probability of chosen 1 person as female can be given as,
[tex]P_A=\dfrac{5}{10} \\P_A=\dfrac{1}{2}[/tex]
Now find the probability of chosen 2nd person as female.
The total females are 4 now and total number of person is remain 9. Thus the probability of chosen 2nd person as female can be given as,
[tex]P_B=\dfrac{4}{9} \\[/tex]
The probability that both people chosen are females can be find out by multiplying both the events as,
[tex]P=P(A)\times P(B)\\[/tex]
Put the values as,
[tex]P(A\capB)=\dfrac{1}{2}\times \dfrac{4}{9}\\P(A\capB)= \dfrac{2}{9}\\[/tex]
Hence the probability that both people chosen are females in the random selection of two people to complete the project is 2/9.
Learn more about the probability here;
https://brainly.com/question/24756209
