Find the probability of selecting either a non-smoker or a woman when you select a person at random from a group composed of 20 female smokers, 50 male smokers, 45 female non-smokers, and 30 male non-smokers.

Answer 1

To find the probability of selecting either a non-smoker or a woman, we need to calculate the total number of non-smokers and women in the group and divide it by the total number of people.

Total number of non-smokers:
45 female non-smokers + 30 male non-smokers = 75 non-smokers

Total number of women:
20 female smokers + 45 female non-smokers = 65 women

Total number of people:
20 female smokers + 50 male smokers + 45 female non-smokers + 30 male non-smokers = 145 people

Now, we can calculate the probability:

P(non-smoker or woman) = (Number of non-smokers + Number of women) / Total number of people
= (75 + 65) / 145
= 140 / 145
≈ 0.9655

Therefore, the probability of selecting either a non-smoker or a woman when selecting a person at random from the group is approximately 0.9655 or 96.55%.