Final Answer:
10. The probability that a person picked at random is either female or has no opinion is the sum of the probability of being female and the probability of having no opinion.
11. The probability that a randomly chosen person said yes, given that the person is male, is the conditional probability of saying yes given male gender.
12. The probability that a randomly chosen person is female and has no opinion is the product of the probability of being female and the probability of having no opinion.
Step-by-step explanation:
10. To find the probability that a person picked at random is either female or has no opinion, sum the individual probabilities of being female and having no opinion.
This is based on the principle that the probability of the union of two mutually exclusive events is the sum of their individual probabilities.
11. The conditional probability of saying yes given that the person is male is found by dividing the probability of the intersection of saying yes and being male by the probability of being male.
This represents the likelihood of saying yes specifically among the male respondents.
12. The probability of a person being female and having no opinion is calculated by multiplying the individual probabilities of being female and having no opinion.
This multiplication is appropriate because these events are assumed to be independent, and the joint probability is the product of their individual probabilities.