Data Analysis and Modeling Techniques (Assignment-1)
2.2, 2.4, 2.6, 2.8, 2.9, 2.10, 2.15, 2.17, 2.19
Suppose that after 10 years of service, 40% of computers have problems
with motherboards (MB), 30% have problems with hard drives (HD), and 15%
have problems with both MB and HD. What is the probability that a 10-year old
computer still has fully functioning MB and HD?
P(MB ∩ HD)=0.15
P(MB U HD) = P(MB)+P(HD)- P(MB ∩ HD)
P(MB U HD) = 0.4 + 0.3 - 0.15
1-P(MB U HD) = 1-0.55
Answer = 0.45 (By taking out all the problem probability from complete
Among employees of a certain firm, 70% know C/C++, 60% know Fortran,
and 50% know both languages. What portion of programmers
(a) does not know Fortran?
(b) does not know Fortran and does not know C/C++?
(c) knows C/C++ but not Fortran? (d) knows Fortran but not C/C++?
(e) If someone knows Fortran, what is the probability that he/she knows C/C++
too? (f) If someone knows C/C++, what is the probability that he/she knows
known values are
P(C) = 0.7
Ans 2.4.a ->
Answer = 1- P(F) = 1-0.6 = 0.4
Ans 2.4.b -> Answer = 1-P(F)-P(C)+P(C∩F) = 1- 0.6 - 0.7 + 0.5 = 0.2
Ans 2.4.c -> Answer = P(C) - P(C∩F) = 0.7 - 0.5 = 0.2
Ans 2.4.d -> Answer = P(F) - P(C∩F) = 0.6 - 0.5 = 0.1
Ans 2.4.e -> Answer = P(C/F) = P(F ∩ C)/P(F) = 0.5/0.6 = 5/6