Answer:
a) there are 2520 possible groups of engineers
b) the probability is 0.76 (76%)
c) the probability is 1/19 ( 5.26%)
Step-by-step explanation:
a) the possible combinations when there is grouping of elements is
C= n!/(a!*b!. ...) , where n= total size and a,b,... = are the group sizes of a ,b and others
in our case , for 8 elements in 4 groups of 2 is
C = 8!/(2!*2!*2!*2!) = 8!/2⁴ = 2520 possible groups of engineers
b) defining the event W= the cellphone works after a week , then the probability is
P(W) = probability that the cellphone is flawed * probability that the cellphone works after a week given that the cellphone is flawed + probability that the cellphone is not flawed * probability that the cellphone works after a week given that the cellphone is not flawed = 0.2 * 0.2 + 0.8 * 0.9 = 0.76
c) the conditional probability can be calculated with the theorem of Bayes. Defining the event F= the design is flawed. Then we have
P(F/W)= P(F∩W)/P(W) = 0.2 * 0.2/0.76 = 1/19 ( 5.26%)
where
P(F∩W) = probability that the design is flawed and the cellphone works after a week
P(F/W)= probability that the design is flawed given the cellphone was still working after a week
