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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 
#2




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: 12 years (.875), 23 years (0.9), 34 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: .....STRAIGHT SURVIVAL. 01 yr = 80 % 02 yr = 60 % 03 yr = 40 % 04 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 % .......SURVIVING THIS INTERVAL 01 yr = 80% 12 yr = 60% 23 yr = 40% 34 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 
The above post was thanked by:  
Doctor Ali (03122013), Evergreen (03122013) 
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