Question

Come up with a real life example which you could use when introducing the formula for calculating the probability of an event occurring to a group of first year students. Using a real life example explain where the formula for conditional probability P(BIA) = P AAT comes from. Hence, or otherwise, explain why, for independent events, the probability of the two events both occurring is the same as the probability of the first event P(A) occurring multiplied by the second event occurring

Answer 1

1) The example of probability:

Let n be the total number of students in first year class.

X be the number of students getting distinction i.e. greater than 75% in the first year class.

Then

Pi be the probability of student getting distinction in first year class=X/n.

2)

Consider the example where

B= no. of people having lung cancer

A= no. of people who smoke

Now we want to compute the probability of people having lung cancer given that he or she smokes.

Here we want to compute the probability of out of all smoking people how many have the lung cancer and this is responsible for the formula of conditional probability.