3. An electrical circuit consists of six electrical devices, A, B and C, which a
ID: 3300488 • Letter: 3
Question
3. An electrical circuit consists of six electrical devices, A, B and C, which are connected in series and are parallel to X, Y and Z. The operation of each type of electrical equipment is independent of each other and is probable. Each type of electrical equipment works as follows.
Equipment
A
B
C
X
Y
Z
Probability to work
0.9
0.8
0.9
0.7
0.8
0.6
a. Find the probability that this circuit will work.
b. If this circuit can work Find the probability that it will work on only one device X.
Equipment
A
B
C
X
Y
Z
Probability to work
0.9
0.8
0.9
0.7
0.8
0.6
Explanation / Answer
a) P(Circuit will work)
= P(A, B and C works and atleast one among X, Y and Z works)
= P(A works)*P(B works)*P(C Works)*P(Atleast one among X, Y and Z works)
= 0.9*0.8*0.9*(1 - P(None of X, Y and Z works))
= 0.9*0.8*0.9*(1 - 0.3*0.2*0.4)
= 0.632448
b) P(Circuit will work only on X | Circuit will work)
= P(A, B, C and X works) / P(Circuit works)
= (0.9*0.8*0.9*0.7)/0.632448 [From part a)]
= 175/244
= 0.7172 [Rounded off to 4 decimal places]