Question

select the correct answer.

in a group of 55 people, 33 are coffee drinkers and 12 are tea drinkers. assuming that no one in this group drinks both tea and coffee, what is the probability that a person picked at random from the group does not drink tea or coffee?

a.

b.

c.

d.

Explanation:

Step1: Find total drinkers

Since no one drinks both, total drinkers = coffee + tea = \(33 + 12 = 45\)

Step2: Find non - drinkers

Total people = 55, so non - drinkers = \(55 - 45 = 10\)

Step3: Calculate probability

Probability = \(\frac{\text{non - drinkers}}{\text{total people}}=\frac{10}{55}=\frac{2}{11}\) (Wait, no, wait. Wait, 55 - 45 is 10? Wait, 33+12 is 45, 55 - 45 is 10? Wait, no, 33 + 12 is 45, 55-45 = 10? Wait, but let's recalculate. 33+12 = 45. 55 - 45 = 10. Then probability is 10/55 = 2/11? Wait, but the options: Wait, maybe I made a mistake. Wait, 33 coffee, 12 tea, total drinkers 33 + 12 = 45. Total people 55. So non - drinkers 55 - 45 = 10. Probability 10/55 = 2/11? Wait, but the options: Let's check the options again. Option D is 2/11? Wait, the user's image: Option D is 2/11? Wait, maybe I miscalculated. Wait, 33 + 12 = 45. 55 - 45 = 10. 10/55 = 2/11. So the correct answer is D. 2/11.

Wait, but let's do it again. Step 1: Number of people who drink coffee or tea (since no overlap) is 33 + 12 = 45. Step 2: Number of people who don't drink either is 55 - 45 = 10. Step 3: Probability is 10/55 = 2/11. So the answer is D. 2/11.

Answer:

D. \(\frac{2}{11}\)