According to a survey 55 of the residents of a city oppose a

According to a survey, 55% of the residents of a city oppose a downtown casino. Of these 55%, about 7 out of 10 strongly oppose the casino.

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.

Solution

First of all, since the value is given as a percentage we will printed that there are only 100 residents.Out of those 100 residents, 55 oppose the casino.

Out of the 55, 7/10 residents strongly oppose the casino.In order to find out how many residents strongly oppose the casino we first 55 by 10 which gives 5.5, then we multiply that by 7 which gives us 38.5. Hence there are 38.5 people who strongly oppose the casino.

Probability of randomly selected resident who oppose the casino and strongly oppose the casino = 38.5/100

probability of the randomly selected resident who oppose the casino but does not strongly oppose the casino = (55-38.5)/100 = 16.5/100

It will not be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino because 38.5% of residents fall into that category.