Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 42​% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts​ (a) and​ (b) below.

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Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 42​% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts​ (a) and​ (b) below.

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Concepts and reason

Probability: The ratio of the number of favorable outcomes to certain event and total number of possible outcomes is called as the probability of an event.

Complementary events: If an event A is defined, then complement of event A is not occurring of event A.

Union of two events: The set of the outcomes that belong to either the two events or any of the two events is called as union of two events.

Intersection of two events: The set of the outcomes that belong to both the two events is called as intersection of two events.

Independent events: Two events A and B are said to be independent events if the occurrence of one event does not affect the occurrence of another event. In other words, if occurring of event A does not influence the event B occurring, then the two events and B are independent.

Fundamentals

The probability of an event is defined as,

P=no of favorable outcomes for an event total number of outcomes 

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