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7. An emergency cooling system consists of a cooling water tank that has cooling water in it about 92% of the time, an emergency cooling water pump that can be counted on to start when needed about 94% of the time, and an emergency cooling water valve that opens when tripped about 96% of the time. Someone will actually push the emergency button in an emergency about 90% of the time, and it will work when pushed about 98% of the time. What is the probability the emergency cooling system will work when needed

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nuhulawal20

Answer:

the probability the emergency cooling system will work when needed is 80.5%

Step-by-step explanation:

 Given the data in the question;

the probability that someone will actually push the emergency button in an emergency from 90% to 99% of the time

E[tex]_4[/tex] ⇒ Someone will actually push the emergency button in an emergency

P(E[tex]_4[/tex]) = 90% = 0.90

E[tex]_4[/tex] : Someone will actually push the emergency button in an emergency

P(E[tex]_4[/tex]) = 99% = 0.99

P(E) = P(E1) × P(E2) × P(E3) × P(E4) × P(E5)

we substitute

P(E) = 92% × 94% × 96%  99% × 98%  

P(E) = 0.8054

P(E) = 80.5%

Therefore, the probability the emergency cooling system will work when needed is 80.5%

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