Each of the depicted systems in the figure consists of 5 ind

Each of the depicted systems in the figure consists of 5 independent elements, each of which functions properly with probability pi, i = 1,..,5. For each of the systems find the probability that the current will flow from the point A to the point B. The first system will work, for example if 1, 2 and 5 are OK; the second system, will work, for example if 1 and 4 function or, say, if 1, 3 and 5 function -i.e., if physically there is a possibility to reach the point B.

Solution

figure A will work if connection 1,2, 5 work or 3,4 ,5 work

now probability of 1 will work = 1/5 and same for others

so 1,2,5 will work probability = (1/5)^3 = 1/125

same for 3,4,5 = 1/125

total probability = 1/125 + 1/125 = 2/125

b) 3 ways are there 1,4, or 2,5 or 1,3,5 or 2,3,4

probability of 1,4 = 1/5*1/5 = 1/25

probability 2,5 = 1/5*1/5 = 1/25

probability 1,3,5 = 1/5^3 =1/125

probability of 2,3,4= 1/5^3 = 1/125

total ptobability = 1/125 + 1/125 + 1/25 + 1/25 = 12/125