Question

Assignment 3 Independence PROBLEM 3.1 (pg 87, #78) A boiler has 5 identical relief values. The probability that any particular value will open on demand is 0.7. Let A, be the event that value i opens,i 1,2,3,4,5. Thus P(A)-0.7. Due Assuming independent operation of the valves, calculate the probability that: a. Odd numbered valves open and the rest fail to open or b. atleast one valve opens AU UA, or PROBLEM 3.2 (pg 87, #80-see diagram below) Consider the system of components in the accompanying picture. Components 3 and 4 are connected in series (call this subsystem 3-4). Subsystem 3-4 will work only if both components 3 and 4 work. In order for the enkire systèr to Tunchion, it must be the case that component 1 functions (A) or compoent 2 functions (A) or bat subsystem 3-4 2 4 functions (A34). Suppose that each individual component functions independently of all other components and each component functions with probability 0.6. Find the probability that the entire system fiunctions or Hint: determine P(A34). It isn't 0.60.

Answer 1

a)P(odd numbered open and rest not opens)=P(1 opens 2 not 3 opens 4 not and 5 opens)

=0.7*0.3*0.7*0.3*0.7=0.03087

b)P(at least one opens)=1-P(none of 5 opens)=1-(0.3)⁵ =0.99757

3.2)

P(system functions)=P(A1 u A2 u A34)=1-P(none of A1 , A2 and A34 works)

=1-(1-0.6)*(1-0.6)*(1-0.6*0.6)=0.8976