Question

according to City high school's alumni records 375 students graduated in college in 2001 are these graduates 176 were female 100 and 47 of whom were accepted into college of the male graduate 100 were accepted to college.A) what is the probability that a 2001 graduate of City high School was accepted into collegeB) what is the probability that 2001 graduate of City high School was not a female C)what is the probability that a 2001 graduate of City high School was accepted into college or maleD) what is the probability of being a female given you were accepted into college.

Answer 1

We are asked to determine probabilities from a population of high school graduates. Let's remember that probability is defined as the quotient of desired events and the number of total events.

a) what is the probability that a 2001 graduate of City High School was accepted into college

To determine the probability we need to find the quotient of the number of students that were accepted into college and the total number of students. The total number of students accepted into college is 145 female plus 100 males, therefore, the probability is:

`P(a)=(145+100)/(375)=(245)/(375)=0.653`

Therefore, the probability is 65.3%.

b)what is the probability that 2001 graduate of City high School was not a female

To do this we will use the fact that the sum of the probabilities that a student is a female plus the probability that the student is not a female must be equal to 1.

`P(\text{female)}+P(\text{not female)=1}`

Therefore, solving for the probability that the student is not a female we get:

`P(\text{not female)=1-P(female)}`

The probability that the student is female is the quotient between the number of female students and the total number of students, therefore:

`\begin{gathered} P(\text{not female)=1-}(176)/(375) \\ \\ P(\text{not female)=1-0.461} \\ P(\text{not female)=0.539} \end{gathered}`

Therefore, the probability that the student is not a female is 53.9%.

c) what is the probability that a 2001 graduate of City high School was accepted into college or male

To determine this probability we need to have into account that the probability of event A or event B happening is the sum of both probabilities minus the probability of both events happening at the same time, therefore:

`P(\text{accepted or male)=P(accepted)+P(male)}-P(\text{accepted and male)}`

Replacing the probabilities we get:

`P(\text{accepted or male)=}0.653+(375-176)/(375)-(100)/(375)`

Solving the operations:

`\begin{gathered} P(\text{accepted or male)=0.653+0.53-0.267} \\ P(\text{accepted or male)=0.916} \end{gathered}`

Therefore, the probability that a student is accepted or male is 91.6%

d) what is the probability of being a female given you were accepted into college.​

The probability of event A given event B is given by the following formula:

`P(A\parallel B)=(P(AandB))/(P(B))`

In this case, we have:

`P(female\parallel accepted)=\frac{P(\text{female and accepted)}}{P(accepted)}`

Replacing the probabilities:

`\begin{gathered} P(female\parallel accepted)=((147)/(375))/(0.653) \\ \\ P(female\parallel accepted)=(0.392)/(0.653) \\ \\ P(\text{female}\parallel accepted)=0.6 \end{gathered}`

Therefore, the probability is 60%.