Question

complete parts (a) through (c). write the probabilities as fractions.
(a) check the outcomes for each event below. then, enter the probability of the event.

	1	2	3	4	5	6	7	8
event a: the selected ball is white	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$\frac{1}{2}$
event b: the selected ball has an even number on it	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$\frac{1}{2}$
event a or b: the selected ball is white or has an even number on it	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$\frac{1}{2}$
event a and b: the selected ball is white and has an even number on it	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$square$	$checkmark$	$\frac{1}{2}$

(b) compute the following.
$p(a)+p(b)-p(a\text{ and }b)=\frac{1}{2}$
(c) select the answer that makes the equation true.
$p(a)+p(b)-p(a\text{ and }b)=p(a\text{ or }b)$

Explanation:

Step1: Identify given probabilities

$P(A)=\frac{1}{2}$, $P(B)=\frac{1}{2}$, $P(A\text{ and }B)=\frac{1}{2}$

Step2: Calculate $P(A)+P(B)-P(A\text{ and }B)$

$P(A)+P(B)-P(A\text{ and }B)=\frac{1}{2}+\frac{1}{2}-\frac{1}{2}=\frac{1}{2}$

Step3: Recall probability formula

The formula for the probability of the union of two events is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ (where $A\cup B$ is $A$ or $B$ and $A\cap B$ is $A$ and $B$). So $P(A)+P(B)-P(A\text{ and }B)=P(A\text{ or }B)$

Answer:

(c) $P(A)+P(B)-P(A\text{ and }B)=P(A\text{ or }B)$