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 5 event a or b: rolling an odd number or rolling a number less than 5 outcomes 1 2 3 4 5 6 probab table with checkboxes for each event (event a, event b, event a or b) and each outcome (1,2,3,4,5,6)

Explanation:

Part (a): Identifying Outcomes and Probabilities

Event A: Rolling an odd number

• Odd numbers on a die: 1, 3, 5.
• Check the boxes for outcomes 1, 3, 5.
• Number of favorable outcomes: 3.
• Total outcomes: 6.
• Probability of Event A: $\frac{3}{6} = \frac{1}{2}$.

Event B: Rolling a number less than 5

• Numbers less than 5: 1, 2, 3, 4.
• Check the boxes for outcomes 1, 2, 3, 4.
• Number of favorable outcomes: 4.
• Total outcomes: 6.
• Probability of Event B: $\frac{4}{6} = \frac{2}{3}$.

Event A or B: Rolling an odd number or a number less than 5

• Outcomes in A or B: 1, 2, 3, 4, 5 (since 1,3,5 are odd; 1,2,3,4 are <5; combined, we exclude 6).
• Check the boxes for outcomes 1, 2, 3, 4, 5.
• Number of favorable outcomes: 5.
• Total outcomes: 6.
• Probability of Event A or B: $\frac{5}{6}$.

Final Answers (Probabilities)

• Event A: $\boldsymbol{\frac{1}{2}}$
• Event B: $\boldsymbol{\frac{2}{3}}$
• Event A or B: $\boldsymbol{\frac{5}{6}}$

Answer:

Part (a): Identifying Outcomes and Probabilities

Event A: Rolling an odd number

• Odd numbers on a die: 1, 3, 5.
• Check the boxes for outcomes 1, 3, 5.
• Number of favorable outcomes: 3.
• Total outcomes: 6.
• Probability of Event A: $\frac{3}{6} = \frac{1}{2}$.

Event B: Rolling a number less than 5

• Numbers less than 5: 1, 2, 3, 4.
• Check the boxes for outcomes 1, 2, 3, 4.
• Number of favorable outcomes: 4.
• Total outcomes: 6.
• Probability of Event B: $\frac{4}{6} = \frac{2}{3}$.

Event A or B: Rolling an odd number or a number less than 5

• Outcomes in A or B: 1, 2, 3, 4, 5 (since 1,3,5 are odd; 1,2,3,4 are <5; combined, we exclude 6).
• Check the boxes for outcomes 1, 2, 3, 4, 5.
• Number of favorable outcomes: 5.
• Total outcomes: 6.
• Probability of Event A or B: $\frac{5}{6}$.

Final Answers (Probabilities)

• Event A: $\boldsymbol{\frac{1}{2}}$
• Event B: $\boldsymbol{\frac{2}{3}}$
• Event A or B: $\boldsymbol{\frac{5}{6}}$