SOLUTION: The probability that a device passes a quality control test is 0.5. Find the probability that a given device will pass the test (a) on the third try (b) after the third try.

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Question 1141829: The probability that a device passes a quality control test is 0.5. Find the probability that a
given device will pass the test
(a) on the third try
(b) after the third try.
Found 2 solutions by VFBundy, greenestamps:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Probability device will pass a quality control test = 0.5
Probability device will fail a quality control test = 0.5

(a) on the third try:

(FAIL)(FAIL)(PASS) = (0.5)(0.5)(0.5) = 0.125

(b) after the third try

(FAIL)(FAIL)(FAIL) = (0.5)(0.5)(0.5) = 0.125

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let Y (yes) and N (no) represent passing or not passing on each try. Then

P(pass on 1st try) = P(Y) = 0.5

P(pass on 2nd try) = P(N,Y) = 0.5*0.5 = 0.25

P(pass on 3rd try) = P(N,N,Y) = 0.5*0.5*0.5 = 0.125

P(pass after the 3rd try) = P(NOT pass on 1st, 2nd, or 3rd try) = 1-(0.5+0.25+0.125) = 0.125