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Old 03-12-2013
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Question Conditional Probability Test

The table shows survival information for patients who had operation for a particular form of cancer (See the attached).
Based on this information if a patient survives for one year, which of the following is the probability that he or she will survive for 4 years

a) 0.875 - 0.8 * 0.9

b) 0.8*0.875*0.9*0.9

c) 0.875*0.9

d) 0.875*0.9*0.9

e) 0.9

f) 0.9 - 0.875
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Old 03-12-2013
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ans. D) 0.875 X 0.9 X 0.9


Short explanation:

Multiply the "% patients surviving this interval" AFTER then ONE year that he already survive...

After the ONE year meaning:
1-2 years (.875),
2-3 years (0.9),
3-4 years ( 0.9)

D) 0.875 X 0.9 X 0.9


Long explanations (if you need further clarifications):

Conditional Probability:....

If given that the pt survived say like 1 yr( or 2 yrs etc.) and asking for probability of surviving certain # of yrs (e.g 2 yrs or 3 yrs etc.).

and the data is given in one of these two ways:


0--1 yr = 80 %
0--2 yr = 60 %
0--3 yr = 40 %
0--4 yr = 20 %

say like if pt survived 1 yr what would be the probability--?(in this case u DIVIDE probability)

DIVIDE by (prob.of # yr pt already survived e.g. 1 yr)

probability of surviving 2 yrs.......60/80 =75%
probability of surviving 3 yrs.......40/80 =50%
probability of surviving 4 yrs.......20/80 =25%

if the pt survived say like 2 yrs and probability of surviving 4 yrs?
20/60 =33 %


0--1 yr = 80%
1--2 yr = 60%
2--3 yr = 40%
3--4 yr = 20%

say like if pt survived 1 yr ,what would be the probability? (in this case MULTIPLY probability.)

Note: Multiply probabilities in between(SKIPPING the survived yr probability in this case 80%)

probability of surviving 3 yrs = 60 times 40
probability of surviving 4 yrs = 60 times 40 times 20

If asked probability of surviving straight say like 4 yrs(from the day one without condition of already survived certain # of yr) = multiply all probabilities 80 times 60 times 40 times 20

answer is D) 0.875 times 0.9 times 0.9

B- would have been the answer if asked straight 4 yr survival

C- is the probability of surviving 3 yrs once the pt already survived for 1 yr
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