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.

event a: rolling an odd number
event b: rolling a number less than 3
event a or b: rolling an odd number or rolling a number less than 3
event a and b: rolling an odd number and rolling a number less than 3

(b) compute the following...

Explanation:

Identify outcomes for Event A

Using the Probability Basics and Theoretical Probability knowledge points

$$ \text{Event A: Rolling an odd number} \implies \{1, 3, 5\} $$

$$ P(A) = \frac{3}{6} = \frac{1}{2} $$

Identify outcomes for Event B

Using the Probability Basics and Theoretical Probability knowledge points

$$ \text{Event B: Rolling a number less than 3} \implies \{1, 2\} $$

$$ P(B) = \frac{2}{6} = \frac{1}{3} $$

Identify outcomes for Event A or B

Using the Probability Basics and Theoretical Probability knowledge points

$$ \text{Event A or B: } \{1, 3, 5\} \cup \{1, 2\} = \{1, 2, 3, 5\} $$

$$ P(A \text{ or } B) = \frac{4}{6} = \frac{2}{3} $$

Identify outcomes for Event A and B

Using the Probability Basics and Theoretical Probability knowledge points

$$ \text{Event A and B: } \{1, 3, 5\} \cap \{1, 2\} = \{1\} $$

$$ P(A \text{ and } B) = \frac{1}{6} $$

Answer:

Event	Outcomes	Probability
Event B: Rolling a number less than 3	Checked: 1, 2	\(\frac{1}{3}\)
Event A or B: Rolling an odd number or rolling a number less than 3	Checked: 1, 2, 3, 5	\(\frac{2}{3}\)
Event A and B: Rolling an odd number and rolling a number less than 3	Checked: 1	\(\frac{1}{6}\)