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Note below that the numbers in brackets listed in the bold titles (e.g. "7.1") indicate which section of the Lecture Notes you might look at to help you answer the questions that follow. Probabilities and Events (7.1) 1. Consider a car which may or may not be working properly. Let \( A \) be the event that the car's engine is working. Let B be the event that the car's air conditioning is working. Given these definitions, write down in mathematical language what is meant by the following: (a) The event that both the car's engine is working. (b) The probability that the car's engine is working. (c) The event that both the car's engine is working and the car's air conditioning is working. (d) The probability that both the car's engine is working and the car's air conditioning is working. (e) The event that the car's engine is working, or the car's air conditioning is working, or both. (Note: normally we would not say "or both".) (f) The probability that the car's engine is working or the car's air conditioning is working. (g) The event that the car's engine is not working. (h) The probability that the car's air conditioning is not working. (i) The probability that both the car's engine and air conditioning are not working.

          Note below that the numbers in brackets listed in the bold titles (e.g. "7.1") indicate which section of the Lecture Notes you might look at to help you answer the questions that follow.

Probabilities and Events (7.1)
1. Consider a car which may or may not be working properly. Let \( A \) be the event that the car's engine is working. Let B be the event that the car's air conditioning is working. Given these definitions, write down in mathematical language what is meant by the following:
(a) The event that both the car's engine is working.
(b) The probability that the car's engine is working.
(c) The event that both the car's engine is working and the car's air conditioning is working.
(d) The probability that both the car's engine is working and the car's air conditioning is working.
(e) The event that the car's engine is working, or the car's air conditioning is working, or both. (Note: normally we would not say "or both".)
(f) The probability that the car's engine is working or the car's air conditioning is working.
(g) The event that the car's engine is not working.
(h) The probability that the car's air conditioning is not working.
(i) The probability that both the car's engine and air conditioning are not working.

Note below that the numbers in brackets listed in the bold titles (e.g. "7.1") indicate which section of the Lecture Notes you might look at to help you answer the questions that follow.

Probabilities and Events (7.1)
1. Consider a car which may or may not be working properly. Let A be the event that the car's engine is working. Let B be the event that the car's air conditioning is working. Given these definitions, write down in mathematical language what is meant by the following:
(a) The event that both the car's engine is working.
(b) The probability that the car's engine is working.
(c) The event that both the car's engine is working and the car's air conditioning is working.
(d) The probability that both the car's engine is working and the car's air conditioning is working.
(e) The event that the car's engine is working, or the car's air conditioning is working, or both. (Note: normally we would not say "or both".)
(f) The probability that the car's engine is working or the car's air conditioning is working.
(g) The event that the car's engine is not working.
(h) The probability that the car's air conditioning is not working.
(i) The probability that both the car's engine and air conditioning are not working.

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