help with math question

Question

1)    (10 points) A group of students are surveyed. Let M be the event that a student is a Mechanical Engineering major. Let C be the event that a student is a Computer Science major. Suppose that

P(M) = 0.28, P(C) = 0.51, and P(M given C) = 0.35.

Find each of the following.

a)    (5 points) Find the probability that a random chosen student double majors in both Mechanical Engineering and Computer Science.

b)    (5 points) Find the probability that a student is a Computer Science major given that he is a Mechanical Engineering major.

Answer 1

Hi Zachary!

Part (a) is asking for P(M and C). To find this, we use the formula P(M and C)=P(M given C)*P(C). We'll plug in the values given in the problem to get P(M and C)=0.35*0.51=0.1785.

Part (b) seeks P(C given M). To find this probability, we can find an equivalent formula for P(M and C) like in part (a) if we rearrange M and C a bit on the right side of the formula: P(M and C)=P(C given M)*P(M). Dividing both sides by P(M) gives P(C given M)=P(M and C)/P(M). We just calculated P(M and C) and we have P(M), so we plug in the values to get P(C given M)=0.1785/0.28=0.6375.

I hope this helps!