Probability

Question

Nonsmokers
men: 328
women: 340
Total:668

Regular Smoker
Men: 80
Women: 60
Total: 140

occasional smoker:
men: 36
women: 37
total:73

Heavy Smoker
Men: 31
Women: 45
Total: 76

Total Men: 475
Total Women: 482
Total: 957

Questions:
-If one of the 957 people is randomly selected, find the probability of getting a regular or a heavy smoker
- Find the probability of selecting someone who is a heavy smoker or is male
- If two different people are randomly selected from the 957 subjects, find the probability that they are both women

Answer 1

For problems like these, it's usually easier to set it up in a table like below. (you can also add tolals if you want)

 

                   Non Smoker     Regular Smoker     Occasional Smoker     Heavy Smoker   

 

Men                  328                  80                           36                           31

Woman             340                  60                           37                           45

 

A. Regular OR Heavy - with OR statments you can add the values, so take the total of all regular and heavy smokers (80+60+31+45) or 216/957

 

B. Same concept as above but since you are going down AND across, need to be careful not to count male heavy smokers twice. (328+80+36+31) for male and add 45 for the additional heavy smoker category. Another way to say that would be (328+80+36+31)+(31+45)-31. Either way, you get 520/957

 

C. Probability of selecting a Woman AND a Woman. With AND statements, we'll multiply the probabilities after finding them. So prob. of selecting a woman on the first pick is (340+60+37+45) = 482/957.

 

Use the same process for selecting the second woman, except there is now 1 less woman (since we picker her the first time). Prob. of this is going to be 481/957. If you multiply 482/957 X 481/957 you get 231,842/915,849 which can be simplified to a fraction using a calculator, or in decimal form, would be approx. 25%.