Question

the table below shows the results of a survey that asked 1053 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).

	males	females	total
oppose	322	291	613
unsure	10	24	34
total	495	558	1053

(a) find the probability that the person opposed the tax or is female. p(opposed the tax or is female) = 0.836 (round to the nearest thousandth as needed.)
(b) find the probability that the person supports the tax or is male. p(supports the tax or is male) = 0.701 (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) = 0.990 (round to the nearest thousandth as needed.)

Explanation:

Step1: Recall probability formula

$P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Step2: For part (a)

The number of people who oppose the tax or are female: The number of females is 558 and the number of males who oppose is 322. So the number of favorable outcomes is $558 + 322=880$. The total number of people is 1053. So $P(\text{opposed the tax or is female})=\frac{880}{1053}\approx0.836$

Step3: For part (b)

The number of people who support the tax or are male: The number of males is 495 and the number of females who support is 243. So the number of favorable outcomes is $495+243 = 738$. The total number of people is 1053. So $P(\text{supports the tax or is male})=\frac{738}{1053}\approx0.701$

Step4: For part (c)

The number of people who are not unsure or are female: The number of unsure people is 34. So the number of non - unsure people is $1053 - 34=1019$. The number of females is 558. But we double - counted non - unsure females. The number of non - unsure females is $558 - 24=534$. The number of non - unsure males is $495 - 10 = 485$. The number of favorable outcomes is $558+(495 - 10)=1043$. So $P(\text{is not unsure or is female})=\frac{1043}{1053}\approx0.990$

Answer:

(a) 0.836
(b) 0.701
(c) 0.990