Question

The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. a juice box is selected at random. what is the probability of the complement of choosing an orange juice box?

a. startfraction 1 over 18 endfraction
b. startfraction 4 over 9 endfraction
c. startfraction 5 over 9 endfraction
d. startfraction 17 over 18 endfraction

Answer 1

The probability of the complement of choosing an orange juice box is 5/9, which is the sum of the probabilities of selecting an apple or fruit punch juice box from the cooler.

Step-by-step explanation:

The question asks for the probability of the complement of choosing an orange juice box from a cooler that contains 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. The total number of juice boxes is 4 (apple) + 8 (orange) + 6 (fruit punch) = 18 juice boxes. The probability of choosing an orange juice box would be the number of orange juice boxes divided by the total number of juice boxes, which is 8/18. However, the complement of this event includes any outcome that is not selecting an orange juice box, which means choosing either an apple or fruit punch juice box. Therefore, we calculate the probability of the complement as the sum of the probabilities of choosing an apple or a fruit punch juice box, which is (4 apple + 6 fruit punch) / 18 = 10/18. Simplifying this fraction gives us 5/9. Thus, the correct answer to the given problem is c. startfraction 5 over 9 endfraction.