Please solve 3.1. Show all steps to the solution. Legible handwriting is desirab

Question

Please solve 3.1. Show all steps to the solution. Legible handwriting is desirable.

Assignment 3 Independence Due PROBLEM 3.1 (pg 87, #78) A boiler has 5 identical relief values. The probability that any particular.yalue will open on demand is 0.7. Let Ai be the event that value i opens, l = 1,2,3,4,5. Thus P(A) = 0.7 Assuming independent operation of the valves, calculate the probability that: Odd numbered valves open and the rest fail to open 4ninAnn4 a. or b. at least one valve opens or 4A 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 entire system to function, it must be the case that component 1 functions (A) or component 2 functions (A2) or that subsystem 3-4

Explanation / Answer

3.1)

P(Ai) = 0.7

P(A1 and A2 ' and A3 and A4' and A5)

= 0.7^3 * (1-0.7)^2    {using independence of Ai s }

= 0.03087

b)

P(A1 or A2 OR A3 OR A4 OR A5)

= 1 - none of them opens

= 1 - (1 - 0.7)^5

= 0.99757

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