Answer:
(a) 0.48
(b) 0.20
(c) it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the casino.
Step-by-step explanation:
(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.
The probability that a radomly selected resident opposes the casino and strongly opposes the cassino is the product of the two probabilities, that a resident opposes the casino and that it strongly opposes the casino (once it is in the first group) as it is shown below.
Use this notation:
- Probability that a radomly selected resident opposes the casino: P(A)
- Probability that a resident who opposes the casino strongly opposes it: P(B/A), because it is the probability of event B given the event A
i) Determine the <em>probability that a radomly selected resident opposes the casino</em>, P(A)
Probability = number of favorable outcomes / number of possible outcomes
- P(A) is <em>given as 60%</em>, which in decimal form is 0.60
ii) Next, determine,the <em>probability that a resident who opposes the casino strongly opposes it</em>, P(B/A):
- It is given as 8 out of 10 ⇒ P(B/A) = 8/10
iii) You want the probability of both events, which is the joint probability or intersection: P(A∩B).
So, you can use the definition of conditional probability:
iv) From which you can solve for P(A∩B)
- P(A∩B) = P(B/A)×P(A) = (8/10)×(0.60) = 0.48
(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.
In this case, you just want the complement of the probability that <em>a radomly selected resident who opposes the casino does strongly oppose the casino</em>, which is 1 - P(B/A) = 1 - 8/10 = 1 - 0.8 = 0.2.
(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino?
You are being asked about the joint probability (PA∩B), which you found in the part (a) and it is 0.48.
That is almost 0.50 or half of the population, so you conclude it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the casino.
