Answer:
(a) P (T|C) = 0.30, P (T|D) = 0.40 and P (O|C) = 0.30
(b) The probability that a death is due to cancer and tobacco is 0.075.
Step-by-step explanation:
Let us denote the events as follows:
C = death is due to cancer
T = cause of cancer was tobacco
D = cause of cancer was diet
O = cause of cancer was other issue
The provided information is:
P (C) = 0.25
P (T|C) = 0.30
P (T|D) = 0.40
P (O|C) = 0.30
(a)
The conditional probability of an event <em>A</em> given that another event <em>B</em> has already occurred is denoted by, P (A|B).
This implies that the occurrence of event B is affected by the previously occurred event A.
Causes of cancer are tobacco, diet and other issues. If a death is caused by cancer then the probability that the cause of cancer was tobacco or diet or something else are conditional events.
The conditional probabilities are:
0.40 for diet, 0.30 for tobacco and 0.30 for other causes.
(b)
Conditional probability formula is:
Compute the probability that a death is due to cancer and tobacco as follows:
Thus, the probability that a death is due to cancer and tobacco is 0.075.