There are three choices of fruit are bananas, pears, and oranges. If the probability of getting a banana is 5/12 and the probability of getting a pear is 1/6, what is the probability of getting an orange?

Question

Responses
A 5/12
B 1/2
C 1/3
D1/12

Answer 1

D 1/12

Explanation:
The total probability of all three fruits must add up to 1. Therefore, if the probabilities of getting a banana and a pear are 5/12 and 1/6 respectively, the probability of getting an orange would be calculated as follows:

Total probability = Probability of getting a banana + Probability of getting a pear + Probability of getting an orange
1 = 5/12 + 1/6 + Probability of getting an orange
1 = 10/12 + 2/12 + Probability of getting an orange
1 = 12/12 (2/12 + Probability of getting an orange)
1 = 2/12 + Probability of getting an orange
1 - 2/12 = Probability of getting an orange
10/12 = Probability of getting an orange
5/6 = Probability of getting an orange

Therefore, the probability of getting an orange is 5/6 or 1/12. Hence, the correct answer is D 1/12.