Suppose that 37% of a community are at least 45 years old.

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Percentage of people in a community who are at least 45 years old is 37%.

Percentage of people who are 45 or older tells the truth is 80%.

Percentage of people who are below 45 tells the truth is 65%.

It is required to obtain the probability that a randomly selected person answers a question truthfully.

Let:

X = Event that a randomly selected person is at least 45 years old.

 = Event that a randomly selected person is below 45.

T = Event that a randomly selected person tells the truth.

The provided information can be written as:

Also,