Question

Problem 1 4.52 Naturalization. The U.S. Bureau of Citizenship and Im- migration Services collects and reports information about natu- ralized persons in Statistical Yearbook. Suppose that a naturalized person is selected at random. Define events as follows: A the person is younger than 20 years old B =the person is between 30 and 64 years old, inclusive, C the person is 50 years old or older, and D the person is older than 64 years. Determine the following events b. (В or D) с. (A & C) а. (пot A) Which of the following collections of events are mutually exclu sive? d. B and C А, В, andD е. f. (not A) and (not D)

Answer 1

given that,

A= the person is younger than 20 years old.

B = the person is between 30 and 64 years old,inclusive,

C = the person is 50 years old or older

D= the person is older than 64 years

The events are as follows,

i) (not A) = the person is 20 years old or older. (ans)

ii) (B or D) = the person is either 30 to 64 years old or the person is older than 64 years.

= the person is 30 years old or older.(ans)

iii) (A & C) = null set, (ans)

Now , we have to find outs the mutually exclusive events,

iv) B and C= the person is 50 to 64 years old.

hence, B and C is not mutually exclusive.

v) A, B and D = null set

as A is the person younger than 20 years, B is a person 30 to 64 years and C is a person older than 64 years.

Hence, this event A,B and D are mutually exclusive.

vi) (not A) = the person is 20 years old or older.

( not D) = the person is up to 64 years old.

not A and not D = the person is 20 to 64 years old.

Hence, the events are not mutually exclusive.

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