You take a test, and 60% pass the first time and 40% fail. The second time around,80% pass the test and 20% fail. The third time, 90% pass and 10% fail.
a. What is the probability that you pass on the 2nd time?
b. What is the probability that you pass on the 3rd time?
c. What is the probability you fail?
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a.
Probability that pass on 2nd time = failed in 1st time x passed in second time
= 0.40 x 0.80= 0.32 or 32/100 = 8/25
b.
Probability that pass on 3rd time = failed in 1st time x failed in 2nd time x passed in 3rd time = 0.4 x 0.2 x 0.9= 0.072 or 72/1000 = 9/125
c.
Probability that pass on 3rd time = failed in 1st time x failed in 2nd time x failed in 3rd time = 0.4 x 0.2 x 0.1= 0.008 or 8/1000 = 1/125
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