According to a survey, 60 % of the residents of a city oppose a downtown casino. of these 60 % about 8 out of 10 strongly oppose the casino. complete parts (a) through (c). (a) find the probability that a randomly selected resident opposes the casino and strongly opposes the casino. (b) find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino. (c) would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino? explain.

(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:

i) Determine the probability that a radomly selected resident opposes the casino, P(A)

Probability = number of favorable outcomes / number of possible outcomes

ii) Next, determine,the probability that a resident who opposes the casino strongly opposes it, P(B/A):

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)

(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 a radomly selected resident who opposes the casino does strongly oppose the casino, 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.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

a

step-by-step explanation: