Question

g circuit operates if and only if there is a path of det to cach other right. The probability of each dev probability that the device operates? ce shown below is indepe 0.7 0.9 0.8

Answer 1

Step 1:

Top 3 devices are in series.

So,

Probability of the system of top 3 devices = 0.9 X 0.8 X 0.7 = 0.5040

Step 2:
Bottom 3 devices are in series.

So

Probability of the system of bottom 3 devices = 0.95³ = 0.8574

Step 3:

Top 3 & Bottom 3 are in parallel.

So,

Probability that the device operates = 1- (1 - 0.5040)(1 - 0.8574)

                                                     = 1- (4960 X 0.1426)

                                                      = 1- 0.0707'

                                                       = 0.9293

So,

Answer is:

0.9293