Question

In a college algebra class of 35 students, there are 20 women and 15 men. On the first exam, 5 women and 4 men received A’s. A student is chosen at random from the class. What is the probability that the student is a man or received an A on the first test? Express your answer as a decimal rounded to four decimal places.

Answer 1

The probability that a student is selected ta random is a man or received an A in the exam is 0.5714.

Explanation:

In a class of 35 students there are 20 women and 15 men.

Compute the probability of selecting a men as follows:

`P(M)=(15)/(35)`

Compute the probability of selecting a women as follows:

`P(W)=(20)/(35)`

It is provided that 5 women and 4 men received A’s in the first exam.

Compute the probability of a a student getting an A and the student being a man as follows:

`P(A\cap M)=(4)/(35)`

Compute the probability of a a student getting an A and the student being a woman as follows:

`P(A\cap W)=(5)/(35)`

Compute the probability of a student receiving an A as follows:

`P(A)=P(M\ca A)+P(W|cap A)=(4)/(35)+(5)/(35) =(9)/(35)`

Compute the probability that a student is selected ta random is a man or received an A in the exam as follows:

`P(M\cap A) = P(M) + P(A) - P (M\cap A)\\=(15)/(35)+(9)/(35)-(4)/(35)\\ =(15+9-4)/(35)\\ =(20)/(35)\\=0.571429\\\approx0.5714`

Thus, the probability that a student is selected ta random is a man or received an A in the exam is 0.5714.