Question

The table below shows the results of a survey that asked 1027 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random. Complete parts​ (a) through​ (c).

	Support	Oppose	Unsure	Total
Males	155	317	99	481
Females	229	291	26	546
Total	384	608	35	1027

1. Find the probability that the person opposed the tax or is female.

2. Find the probability that the person supports the tax or is male.

3. ​Find the probability that the person is not unsure or is a female.

Answer 1

1. Answer :

P(opposed or female) = P(opposed) + P(female) - P(opposed and female)   ............(addition rule of probability)

                                    = (608 / 1027) + (546 / 1027) - (291 / 1027)

                                    = 863 / 1027

                                    = 0.8403

Therefore, the probability that the person opposed the tax or is female is 0.8403

2. Answer :

P(supports or male) = P(supports) + P(male) - P(supports and male)     ............(addition rule of probability)

                                 = (384 / 1027) + (481 / 1027) - (155 / 1027)

                                 = 710 / 1027

                                 = 0.6913

Therefore, the probability that the person supports the tax or is male is 0.6913

3. Answer :

P(not unsure or female) = P(not unsure) + P(female) - P(not unsure and female)     .....(addition rule of probability)

                                       = ((1027 - 35) / 1027) + (546 / 1027) - ((229 + 291) / 1027)

                                       = (992 / 1027) + (546 / 1027) - (520 / 1027)

                                       = 1018 / 1027

                                       = 0.9912

Therefore, the probability that the person is not unsure or is a female is 0.9912