A beverage manufacturer would like to test the reliability of two processes for manufacturing orange juice and apple cider, respectively. A review of the orange juice manufacturing process found that 10% of the bottles are underfilled. A review of the apple cider manufacturing process found that 15% of the bottles are underfilled.

	Orange Juice	Apple Cider
Probability of under-fill	0.10	0.15

If two cans are selected at random (one from each process), what is the probability of selecting one under filled orange juice bottle and one under filled apple cider bottle?

Explanation

Let P(A) be the probability of selecting an under-filled orange juice bottle. Let P(B) be the probability of selecting an under-filled apple cider bottle.

For independent events, those that do not influence the probability of the other occurring, the probability of events A and B occurring is given by the formula:
 
P(A and B)=P(A)∗P(B)
The two events are independent because selecting an under-filled bottle from the orange juice lot does not affect the probability of selecting an under-filled bottle from the apple cider lot. Substitute the given values and evaluate their product to find the probability of selecting both:
P(A and B)=0.10∗0.15
P(A and B)=0.015