An electronic scanner is successful in detecting flaws in a

An electronic scanner is successful in detecting flaws in a material in 80% of the cases. Three material specimens containing flaws will be tested with the scanner. Assume that the tests are independent.

Find the probability that the scanner is successful in exactly two of the three cases.
Find the probability that the scanner is successful in at least two of the three cases.

Please include all steps with the answer

Solution

the probability of detecting flaws = .8
the probability of not detecting flaws = .2

let
D= scanner detected flaw
N= scanner didn\'t detect flaw

Outcomes
DDD=.8^3=.512
DDN=.8^2*.2=.128
DND=.128
NDD=.128
NND
NDN
DNN
NNN

P(DDD or DDN or DND or NDD)=3*.128+.512=.896

89.6% Probability that the detector is successful at least two out three