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Question

At a local college, 183 of the male students are smokers and 427 are non-smokers. Of the female students,252 are smokers and 348 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?

Answer 1

Hi Rae,

 

Here is how to visualize the problem

 

                             Males                     Females               Total

                          .................             ..................        ..............

 

Smokers                  183                          252                 435

 

 

Non-Smokers           427                          348                 775

 

Total                       610                           600                1210

 

 

A = the event that a student is male and a smoker, P(A)=183/1210

 

B = the event that a student is female and a smoker, P(B) =252/1210

 

P(A and B) = P(A)P(B) = (183/1210)*(252/1210) =0.0315

 

 

 

Answer 2

Take the probability of choosing a male smoker:

 

183/610 = 3/10

 

Since you must pick a male and female student, and not just a random student from the total pool of 1210 students, the final probability would be.

 

(3/10) * (252/600) = (3/10)*(21/50) = (63/500) ≈ 0.126

 

These are independent probabilities, as in, the probability of one does not affect the probability of the other. It can be expressed as

 

P(A AND B) = P(A)*P(B)

 

So, the approximate probability of picking a male and female smoker at random from the of all students will be 0.126. The exact probability is 63/500.