Problem 11P

A total of 28 percent of American males smoke cigarettes, 7 percent smoke cigars, and 5 percent smoke both cigars and cigarettes.

(a) What percentage of males smokes neither cigars .nor cigarettes?

(b) What percentage smokes cigars but not cigarettes?

Solution :

Step 1 of 2:

Let S be the event that a randomly chosen American made smoke cigarettes and E be the event that a randomly chosen American male smoke cigarettes.

From the given information

P(E) =

P(E) = 0.28

P(S) =

P(S) = 0.07

Then the P(AS) is

P(ES) =

P(ES) = 0.05

Our goal is:

a). We need to find percentage of males smokes neither cigars .nor cigarettes.

b). We need to find percentage smokes cigars but not cigarettes.

a). The probability that a randomly chosen American male smokes neither cigars nor cigarettes.

P() =

P() = 1-P(SE)

P() = 1-P(S)-P(E)+P()

P() = 1-0.07-0.28+0.05

P() = 0.7

Here 0.7100 = 70%.

Therefore, 70 percentage of males smokes neither cigars .nor cigarettes.