A parallel system is composed of n separate components. The system functions whe

Question

A parallel system is composed of n separate components. The system functions when at least one of the components functions. Suppose the following systems function if current flows from A to B. If each switch (break in the line) is activated (i.e. closed to allow electricity to flow across the line) independently with probability p = 0.6, what is the probability the system functions? Solve for each circuit. (Note: for circuit a, there are 4 components labeled 1, 2, 3, and 4. There is one switch per component. For circuit b, there are 3 components labeled 1, 2, and 3. Component 1 has 2 switches, component 2 has one switch and component 3 has 3 switches).

stat purdue.edu 1H4 Leiyi Pan Chegg Study Guide. STAT 225 Course Int www.stat purdue ed Homework www.stat purdue.ed LON-CAPA HW 6:Th e) What is the probability that a student takes exactly 2 languages? f) What is the probability a student takes all 3 languages or no language at all? g) Given that a student takes Chinese, what is the probability that the student takes Spanish? 2. A parallel system is composed of n separate components. The system functions when at least one ofthe components functions. Suppose the following systems function if current flows from Ato B. If each switch (break in the line) is activated (i.e. closed to allow electricity to flow across the line) independently with probability p 0.6, what is the probability the system functions? Solve for each circuit. (Note: for circuit a, there are 4 components labeled 1, 2, 3, and 4. There is one switch per component. For circuit b, there are 3 components labeled 1, 2, and 3. Component 1 has 2 switches, component 2 has one switch and component 3 has 3 switches).

Explanation / Answer

a)probabilty that system will work =P( at least one component does function) =1-P(none of the component functions)

=1-(1-0.6)4 =0.9744

b) for curcuit B;

probabilty that component 1 will work =P(both the switch will work) =0.6*0.6 =0.36

probabilty that component 2 will work =0.6

probabilty that component 3 will work =P(all three switches work) =0.6*0.6*0.6 =0.216

probabilty that system will work =P( at least one component does function) =1-P(none of the component functions)

=1-(1-0.36)*(1-0.6)*(1-0.216) =1-0.2007 =0.7993

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