Question

Suppose we have a sample of 7445 naturalized US citizens. We have the events given in the table below. Suppose we choose someone from this group at random events.

(a) Find P(A) Event Size

(b) Find P(Ac ) A under 20 2450

(c) Find P(B) B 30 to 64 1850

(d) List all pairs of events that are mutually exclusive. C 50 + 2125

(e) Find P(A or B) D 65 + 1020

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Event & Size \\ \hline A & Under\ 20 & 2450 \\ \hdashline B & 30\ to\ 64 & 1850 \\ \hdashline C & 50\ +\ & 2125 \\ \hdashline D & 65\ + & 1020 \end{array}$$

(a)

$$P(A)=\dfrac{2450}{7445}=\dfrac{490}{1489}$$

(b)

$$P(A^C) =1-P(A)=1-\dfrac{490}{1489}=\dfrac{999}{1489}$$

(c)

$$P(B)=\dfrac{1850}{7445}=\dfrac{370}{1489}$$

(d)

A and B, A and C, A and D, B and C, B and D, C and D

(e)

$$P(A\ or\ B)=P(A\cup B)=P(A)+P(B)$$

$$=\dfrac{490}{1489}+\dfrac{370}{1489}=\dfrac{860}{1489}$$