The table below shows the results of a survey that asked 1062 adults from a cert
ID: 3294574 • Letter: T
Question
The table below shows the results of a survey that asked 1062 adults from a certain country if they would support a change in their country's flag. A person is selected at random. Complete parts (a) through (d). (a) Find the probability that the person opposed the change or is female. P(opposed the change or is female) = (Round to the nearest thousandth as needed.) (b) Find the probability that the person supports the change or is male. P(supports the change or is male) = (Round to the nearest thousandth as needed.) (c) Find the probability that the person is not unsure or is female. P(is not unsure or is female) = (Round to the nearest thousandth as needed.) (d) Are the events "being male" and "support" mutually exclusive? Explain. A. Yes, because one can't be male and support the change at the same time. B. Yes, because there are 156 males that support the change. C. No, because there are 156 males that support the change. D. No, because one can't be male and support the change at the same time.Explanation / Answer
a) Probability that opposed change or female = Probability that opposed change + Probability of female - Probability (opposed change and a female)
Probability that opposed change or female = 642/1062 + 559/1062 - 307/1062 = 894/1062 = 0.842
b)
Probability that support change or male = Probability that support change + Probability of male - Probability (support change and a male)
Probability that support change or male = 384/1062 + 503/1062 - 156/1062 = 894/1062 = 0.688
c)
Probability that not unsure or female = Probability that not unsure + Probability of female - Probability (not unsure and a female)
Probability that not unsure or female = 559/1062 + 1026/1062 - (559-24)/1062 = 1050/1062 = 0.989
d) In logic and probability theory, two propositions (or events) are mutually exclusive or disjoint if they cannot both be true (occur).
So, C option as both can occur at same time.
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