6. The workers in a factory need to attend a competency course and pass three tests. The probability of passing the first test is 0.8 and if worker passes a test, the probability that the worker will pass the subsequent test is 0.9. On the other hand, if the worker fails, the probability that the worker will fail the subsequent test is 0.7. a) Construct a tree diagram for the events above. b) Find the probability that a worker will pass the first and the third test. c) Find the probability that a worker will pass at least two test.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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6. The workers in a factory need to attend a competency course and pass three tests. The probability of passing
the first test is 0.8 and if worker passes a test, the probability that the worker will pass the subsequent test is
0.9. On the other hand, if the worker fails, the probability that the worker will fail the subsequent test is 0.7.
a) Construct a tree diagram for the events above.
b) Find the probability that a worker will pass the first and the third test.
c) Find the probability that a worker will pass at least two test.
Transcribed Image Text:6. The workers in a factory need to attend a competency course and pass three tests. The probability of passing the first test is 0.8 and if worker passes a test, the probability that the worker will pass the subsequent test is 0.9. On the other hand, if the worker fails, the probability that the worker will fail the subsequent test is 0.7. a) Construct a tree diagram for the events above. b) Find the probability that a worker will pass the first and the third test. c) Find the probability that a worker will pass at least two test.
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