Question

complete parts (a) through (c).

(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

Event A is "Rolling an odd number".
Outcomes: 1, 3, 5.
Number of outcomes: 3.
Probability:

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

Identify outcomes for Event B

Event B is "Rolling a number less than 3".
Outcomes: 1, 2.
Number of outcomes: 2.
Probability:

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

Identify outcomes for Event A or B

"Event A or B" is the union of outcomes from A and B.
Outcomes: 1, 2, 3, 5.
Number of outcomes: 4.
Probability:

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

Identify outcomes for Event A and B

"Event A and B" is the intersection of outcomes from A and B.
Outcomes: 1.
Number of outcomes: 1.
Probability:

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

Answer:

Question 1

• Event A: Rolling an odd number
• Outcomes checked: 1, 3, 5
• Probability: \(\frac{1}{2}\)

Question 2

• Event B: Rolling a number less than 3
• Outcomes checked: 1, 2
• Probability: \(\frac{1}{3}\)

Question 3

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

Question 4

• Event A and B: Rolling an odd number and rolling a number less than 3
• Outcomes checked: 1
• Probability: \(\frac{1}{6}\)