4.30 Support for casino in Toronto. In an effort to seek the public's input on the establishment of a
casino, Toronto's city council enlisted an independent
analytics research company to conduct a public survey.
A random sample of 902 adult Toronto residents were
asked if they support the casino in Toronto. Here are
the results:
Response
Strongly
support
0.16
Somewhat
support
0.26
Mixed
feelings
Probability
?
Response
Somewhat
oppose
0.14
Strongly
oppose
0.36
Don't
know
0.01
Probability
(a) What probability should replace "?" in the distribution?
(b) What is the probability that a randomly chosen adult
Toronto resident supports (strongly or somewhat) a casino?

a) 7% or 0.07

b) 42% or 0.42

Explanation:

Let's begin by listing out the given information:

Population = 902,

Probability distribution

Strongly support = 0.16 or 16%,

Somewhat support = 0.26 or 26%,

Mixed feelings = ?,

Somewhat oppose = 0.14 or 14%,

Strongly oppose = 0.36 or 36%

Don't know = 0.01 or 1%

a) The summation of every probability of an event (survey) is 100% ⇒ Pr (survey) = 100%

Pr (survey) = Pr [strongly support + somewhat support + mixed feelings + somewhat oppose + strongly oppose + don't know]

100 = 16 + 26 + x + 14 + 36 + 1

To obtain the probability of the 'Mixed feelings' populace, we subtract the summation of all other probabilities from 1 or 100%

x = 100 - (16 + 26 + 14 +36 + 1) = 100 - 93

x = 7% or 0.07

∴ the probability of the 'Mixed feelings' populace is 7% or 0.07

b) Probability of a random adult supporting is given by the summation of the probabilities of the adults who strongly support & those who somewhat support

Pr (support) = Pr (strongly support) + Pr (somewhat support)

Pr (support) = 0.16 + 0.26

Pr (support) = 0.42 or 42%

∴ the probability that a randomly chosen adult supports the casino in Toronto is 42%

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answer; ///(d); determining who competes most closely   with whom evaluating whether industry driving forces and competitive pressure favor some strategic groups and hurt others, and ascertaining whether the profit potential of different strategic groups varies due to the strengths and weaknesses in each groups respective market positions;