You are hired by your local member of parliament to conduct a survey on unemployment, crime,
taxes and mail delivery. You make up a question on each topic for your survey sheet. If the
questions are arranged in random order on the sheet, find the probability of each of the following.
(a) The question about mail delivery will be first.
(b) The question about mail delivery will be first and the question on crime will be second.
Thanks
(a) 1/4
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
(b) 1/4 * 1/(4-1) = ?
To find the probability of each scenario, we need to consider the number of possible arrangements of the questions and divide it by the total number of possible arrangements.
We have four topics: unemployment, crime, taxes, and mail delivery. Since the questions are arranged in a random order, there are 4! (4 factorial) possible arrangements, which is equal to 4 x 3 x 2 x 1 = 24.
(a) The question about mail delivery will be first.
Since there are four topics and only one question about mail delivery, there is only one possible arrangement where the question about mail delivery is first. Therefore, the probability is 1/24.
(b) The question about mail delivery will be first and the question on crime will be second.
There are two conditions to satisfy this scenario: the question about mail delivery being first and the question on crime being second. Since there is only one question about mail delivery and there is only one question on crime, the probability of both conditions being satisfied is 1/24.
So, the probability for both scenarios is 1/24.