Final answer:
When calculating the combined probability of choosing one baby with no hair and another with a little hair from the local hospital, the rules of probability and combination of events are applied, yielding a 1/4 chance. This is the sum of the probabilities of the two possible selection orders, resulting in option B. 1/4 as the correct answer.
Step-by-step explanation:
To find the probability that one of the two randomly chosen babies has no hair and the other has a little hair, we need to consider the probabilities of each event and use the rules of probability for combined events.
A quarter of the babies are born with no hair, which is a probability of ¼, and half the babies are born with a little hair, which is a probability of ½. The rest of the babies, which would be ¼, are born with a lot of hair, but this is irrelevant to the question.
In this scenario, since there are two distinct events — choosing a baby with no hair and choosing a baby with a little hair — we use the product rule of probability where we multiply the probability of each independent event. However, since the order does not matter (it could be first no hair and then a little hair, or first a little hair and then no hair), we must consider both possibilities.
- Probability of first choosing a baby with no hair and then one with a little hair: (¼) × (½).
- Probability of first choosing a baby with a little hair and then one with no hair: (½) × (¼).
Since these are two separate ways that the desired outcome can occur, we use the sum rule of probability to combine them: (¼ × ½) + (½ × ¼).
Calculating this gives: (1/4 × 1/2) + (1/2 × 1/4) = 1/8 + 1/8 = 2/8 or simplified to 1/4.
The correct answer is B. 1/4, which is the probability of choosing one baby with no hair and another with a little hair from the local hospital.