Applications of probability
We can use theoretical probability of an event to predict the results of experiments. The expected outcome is the probability of the outcome multiplied by the number of trials.
We can then compare expected results with actual results and make judgments.
The financial expectation gives an indication on expected gains using the probability and value of each outcome. Calculating financial expectation gives an idea about whether the venture is viable or not.
It is calculated by multiplying each financial outcome by its probability.
A negative value is a financial loss.
If there is a fixed cost, this needs to be taken into account also.
Two-way tables can be used when there are exactly two possibilities for each of two outcomes. This is often in the form of negative/positive result.
The test result can either be accurate (true positive/true negative) or inaccurate (false positive/false negative).
In a two-way table, there are two possible results for each of the two tests, therefore four total possible outcomes.
QUESTIONS:
Q1.
Over the past 20 years it has been noted that in the Australian snowfields there is sufficient snow for skiing on 72% of days during ski season.
If ski season is June, July, August and September, how many skiable days can be expected?
Emma buys a ticket in a raffle. There are 200 tickets in the raffle and two prizes. First prize is $100 and second prize is $50. Tickets are $2 each of 3 for $5.
a) Find Emma's financial expectation if she buys one ticket for $2.
b) Would her financial expectation improve if she buys 3 for $5?
A die is rolled 300 times.
a) How many sixes can we expect to be rolled?
b) If 45 sixes are rolled in 300 trials would you, believe the die is biased? Explain your answer.
A new test is being developed to detect the presence of illegal performance-enhancing drugs in athletes. A sample of 50 mice was selected from a total of 200 mice and given an illegal drug. All 200 mice were then tested for the drug. Of the drugged mice, 2 gave an inaccurate test result. From the mice without the drug, there were 18 false positives.
a) Present the data in a two way table.
b) A researcher takes a mouse from the batch.
(i)What is the probability that this mouse had the drug?
(ii)What is the probability that this mouse returned a negative test result for the drug?
