Question

Use the table to answer the following question.

	Male(M)	Female(F)	Total
Smoker(S)	60	70
Non-smoker(NS)	40	50
Total

P(M) = P(S) =

P(M|S) = P(S|F) =

P(F or S) = P(F and NS) =

Answer 1

The table above summarizes the data on smokers and non-smokers and the proportion of them being either males or females.

We shall first total each row and each column. Doing so, we get:

	Male (M)	Female (F)	TOTAL
Smokers (S)	60	70	130
Non-smoker (NS)	40	50	90
TOTAL	100	120	220

P(M) refers to the proportion of the males in the total candidates and P(F) refers to the proportion of the females in the total candidates.

Hence, P(M) and P(F) becomes:

Next, we have to determine the probabilities P(M|S) and P(S|F). These are conditional probabilities.

A conditional probability P(A|B) is the probability of A and B divided by the probability of B.

Hence, the formula of P(A|B) is:

Now and refers to when both the events A and B are occurring. Therefore, we can now determine the desired probabilities. We get:

P(F or S) refers to the probability of either F or S occurring, This is depicted symbolically as:

Now these events are not independent. Hence, the probability of this event can be determined using the formula as:

Substituting the values from the table, we get:

P(F and NS) refers to the event where both of these are occurring and hence refers to the cell that corresponds to both these events.

Therefore, the probability becomes: