Questions: The table below shows the results of a survey that asked 1056 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 151 323 11 485 Females 245 302 24 571 Total 396 625 35 1056 (a) Find the probability that the person opposed the tax or is female. P (opposed the tax or is female) = .847 (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) = .691 (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.)

The table below shows the results of a survey that asked 1056 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 151 323 11 485
Females 245 302 24 571
Total 396 625 35 1056

(a) Find the probability that the person opposed the tax or is female.

P (opposed the tax or is female) = .847
(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) = .691
(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.)

Transcript text: The table below shows the results of a survey that asked 1056 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). \begin{tabular}{rcccc} & Support & Oppose & Unsure & Total \\ Males & 151 & 323 & 11 & 485 \\ Females & 245 & 302 & 24 & 571 \\ Total & 396 & 625 & 35 & 1056 \end{tabular} (a) Find the probability that the person opposed the tax or is female. P (opposed the tax or is female) $=.847$ (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) $=.691$ (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.)

Solution

Solution Steps

Step 1: Calculate total probabilities for each category

$ P(M) = \frac{N_m}{N} = \frac{485}{1056} = 0.459 $ $ P(F) = \frac{N_f}{N} = \frac{571}{1056} = 0.541 $ $ P(S) = \frac{S}{N} = \frac{396}{1056} = 0.375 $ $ P(O) = \frac{O}{N} = \frac{625}{1056} = 0.592 $ $ P(U) = \frac{U}{N} = \frac{35}{1056} = 0.033 $

Step 2: Calculate probabilities for composite events

$ P(M \cap S) = \frac{S_m}{N} = \frac{151}{1056} = 0.143 $ $ P(F \cap O) = \frac{O_f}{N} = \frac{302}{1056} = 0.286 $ $ P(\text{not U}) = 1 - P(U) = 1 - 0.033 = 0.967 $ $ P(F \cap U) = \frac{U_f}{N} = \frac{24}{1056} = 0.023 $

Step 3: Adjust for overlapping categories and calculate final probabilities

$ P(S \cup M) = P(S) + P(M) - P(S \cap M) = 0.375 + 0.459 - 0.143 = 0.691 $ $ P(O \cup F) = P(O) + P(F) - P(O \cap F) = 0.592 + 0.541 - 0.286 = 0.847 $ $ P(\text{not U} \cup F) = P(\text{not U}) + P(F) - P(F \cap U) = 0.967 + 0.541 - 0.023 = 1.485 $

$P \leq 1$ $P(\text{not U} \cup F) = 1$

Final Answer:

The detailed probabilities for the given survey data are calculated with the specified precision of 3 decimal places.

LaTeX Format of Calculations:

$ P(\text{supports the tax or is male}) = P(S) + P(M) - P(S \cap M) = 0.375 + 0.459 - 0.143 = 0.691 $ $ P(\text{opposed the tax or is female}) = P(O) + P(F) - P(O \cap F) = 0.592 + 0.541 - 0.286 = 0.847 $ $ P(\text{not unsure or is female}) = P(\text{not U}) + P(F) - P(F \cap U) = 1 $

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!