A total of 28 percent of American males smoke cigarettes, 7...

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?

Transcript

00:01 This problem is said that a total of 28 % of american males smoke cigarettes, 7 % smoke cigars, and 5 % smoke both cigars and cigarettes.

00:12 We need to use this information to find certain percentages.

00:17 So let us consider the event that a male smokes cigarettes is a, and let us consider b to be the event that a person smokes cigars.

00:26 So b is for cigars, and a is for cigarettes.

00:34 So it is given that 28 % smoke cigarettes.

00:38 So the probability of this event a is 28 % or 0 .28.

00:44 7 % smoke cigar.

00:46 So p of b is 7 % or 0 .07.

00:50 And it is said that 5 % smoke both.

00:53 So p of a, intersection b.

00:56 So that's the probability of a and b.

00:58 That is 5 % or 0 .05.

01:01 Now let us use this information.

01:03 To determine the given probabilities.

01:06 We need to find the percentage of male smoking neither cigars nor cigarettes.

01:09 So let us find the probability that a person does not smoke cigars and does not smoke cigarettes.

01:16 So a person doesn't smoke cigarettes means a bar, that's a complement, and b bars.

01:22 So that doesn't smoke cigars.

01:25 So if you have a bar intersection b bar, if we use d.

01:29 Morgan's law, then a bar intersection b bar is a union b.

01:33 Bar.

01:35 So we will have 1 minus p of a union b and p of a union b is given by p a plus p b minus p of a intersection b...

Question

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?

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