Question

7. The following diagram is a segment of a printed circuit which has eight relays, used in a computer mother-board. Current will flow from point "a" to point "b" if there is at least one closed path when the relays are switched to "close". However, the relays may malfunction. Suppose each relay closes properly only with probability .80 when the switch is thrown, and suppose they operate independently of one another. ------(3) a*(1)(2) ----(5)----- ------(4)-------- --(6)---------- -(7)- ------(8) b a. Let $A_i$ denote the event that the $i$th switch closes properly when the switches are thrown ($i=1,...,8$) and B denote the event that current can flow from point a to point b. Express event B in terms of event A's and then find the probability that current can flow from point a to point b. That is, find $P(B)$. b. If the system is working, find the probability that the component 4 is working. That is, find $P(A_4 | B)$. c. Are events B and $A_i$ independent? Check!

          7.
The following diagram is a segment of a printed circuit which has eight relays, used in a computer mother-board. Current will flow from
point "a" to point "b" if there is at least one closed path when the relays are switched to "close". However, the relays may malfunction.
Suppose each relay closes properly only with probability .80 when the switch is thrown, and suppose they operate independently of one
another.
------(3)
a*(1)(2)
----(5)-----
------(4)--------
--(6)----------
-(7)-
------(8) b
a.
Let $A_i$ denote the event that the $i$th switch closes properly when the switches are thrown ($i=1,...,8$) and B denote the event that current
can flow from point a to point b. Express event B in terms of event A's and then find the probability that current can flow from point a
to point b. That is, find $P(B)$.
b.
If the system is working, find the probability that the component 4 is working. That is, find $P(A_4 | B)$.
c.
Are events B and $A_i$ independent? Check!

7.
The following diagram is a segment of a printed circuit which has eight relays, used in a computer mother-board. Current will flow from
point "a" to point "b" if there is at least one closed path when the relays are switched to "close". However, the relays may malfunction.
Suppose each relay closes properly only with probability .80 when the switch is thrown, and suppose they operate independently of one
another.
——(3)
a*(1)(2)
—-(5)—–
——(4)——–
–(6)———-
-(7)-
——(8) b
a.
Let Ai denote the event that the ith switch closes properly when the switches are thrown (i=1,...,8) and B denote the event that current
can flow from point a to point b. Express event B in terms of event A's and then find the probability that current can flow from point a
to point b. That is, find P(B).
b.
If the system is working, find the probability that the component 4 is working. That is, find P(A4 | B).
c.
Are events B and Ai independent? Check!

Added by Emily N.

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