# Probability Problem

Q:  Problems of sexual harassment recieved much attention in recent years. In one survey, 420 workers (240 of whom are men) considered a friendly pat on the shoulder to be sexual harassment, whereas 580 workers (380 of whom are men) did not consider it to be a form of harassment. Find the probability of randomly selecting a man or someone who does not consider a pat on the shoulder to be a form of sexual harassment.

A:  This problem might have some interpretation issues (depending on how you read it)… Here is how I read the question, which I believe is the correct way:

Find the probability of randomly selecting a man or someone who does not consider a pat on the shoulder as sexual harassment.

OK… Now we need a formula (that you should know!):

P(A or B) = P(A) + P(B) – P(A and B)

So, let’s put our words into this problem:

P(man or someone who does not consider a pat on the shoulder as sexual harassment) = P(Man) + P(someone who does not consider a pat on the shoulder as sexual harrasment)P(man and someone who does not consider a pat on the shoulder as sexual harassment)

I know, that is one long equation!  But, it is important to see it in words… I color coded it for ease:

P(Man) = (total men) / (total people) = (240 + 380) / (420 + 580) = 620/1000 = 31/50

P(someone who does not consider a pat on the shoulder as sexual harrasment) = (people who think sex harassment) / (total people) = 420/1000 = 21/50

The red part is the last piece of the puzzle we need and the hardest part to find… This part is ALL MEN who think that a pat is sexual harassment.  The problem says that that is 240 men… So,

P(man and someone who does not consider a pat on the shoulder as sexual harassment) = 240/1000 = 6/25

Now, plug it all in:

P(man or someone who does not consider a pat on the shoulder as sexual harassment) = 31/50 + 21/50 – 6/25 = 4/5

Questions?