Probability Questions Question 2 Are the events girl and sop

Probability Questions:

Question #2: Are the events \"girl\" and \"sophomore\" independent?

Question #3: Are the events \"girl\" and \"junior\" independent?

Question #4: Two students are selected at random from the school without replacement. What is the probability that they are both boys?

FreshmenSophomores Juniors Seniors Total Boys Girls Total 28 32 60 7 8 7 10 16 15 12 17

Solution

Question #1: What is the probability that a randomly selected student is a girl given that the student is a sophomore?

Directly from the table,

P(G|S) = 8/15

Question #2: Are the events \"girl\" and \"sophomore\" independent?

If they are independent,

P(G|S) = P(G)

As

P(G) = 32/60 = 8/15

Then YES, THEY ARE INDEPENDENT.

Question #3: Are the events \"girl\" and \"junior\" independent?

If they are independent,

P(G|J) = P(G)

From the table,

P(G|J) = 7/12 =/= 8/15

Thus, they are not independent.

Question #4: Two students are selected at random from the school without replacement. What is the probability that they are both boys?

There are 60C2 = 1770 ways to pick 2 students.

There are 28C2 = 378 ways to pick 2 boys.

Hence

P(both boys) = 378/1770 = 0.213559322 [answer]