Question

number cube is rolled three times. an outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). the 8 outcomes are listed for each of the three events below. note that each outcome has the same probability.
for each of the three events below, select all outcomes that are contained in the event. then enter the probability of the event.
(a) event a: two or more even numbers
select all outcomes that are contained in event a.
□ oee □ eeo □ oeo □ eoo □ ooo □ ooe □ eoe □ eee
find the probability of event a.
probability: □
(b) event b: an even number on the first roll or the third roll (or both)
select all outcomes that are contained in event b.
□ oee □ eeo □ oeo □ eoo □ ooo □ ooe □ eoe □ eee
find the probability of event b.
probability: □
(c) event c: an odd number on each of the first two rolls
select all outcomes that are contained in event c.
□ oee □ eeo □ oeo □ eoo □ ooo □ ooe □ eoe □ eee
find the probability of event c.

Explanation:

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Part (a) Event A

Step1: Identify valid outcomes

Outcomes with ≥2 even numbers: EEO, EOO, EOE, EEE

Step2: Count valid outcomes

Count = 4

Step3: Total possible outcomes

Total = 8

Step4: Calculate probability

$\text{Probability} = \frac{\text{Valid Outcomes}}{\text{Total Outcomes}} = \frac{4}{8} = \frac{1}{2}$

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Part (b) Event B

Step1: Identify valid outcomes

Outcomes with even on 1st/3rd (or both): OEE, EEO, EOO, EOE, EEE

Step2: Count valid outcomes

Count = 5

Step3: Total possible outcomes

Total = 8

Step4: Calculate probability

$\text{Probability} = \frac{\text{Valid Outcomes}}{\text{Total Outcomes}} = \frac{5}{8}$

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Part (c) Event C

Step1: Identify valid outcomes

Outcomes with odd on first two rolls: OEE, OEO, OOO, OOE

Step2: Count valid outcomes

Count = 4

Step3: Total possible outcomes

Total = 8

Step4: Calculate probability

$\text{Probability} = \frac{\text{Valid Outcomes}}{\text{Total Outcomes}} = \frac{4}{8} = \frac{1}{2}$

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Answer:

(a) Selected outcomes: EEO, EOO, EOE, EEE; Probability: $\frac{1}{2}$
(b) Selected outcomes: OEE, EEO, EOO, EOE, EEE; Probability: $\frac{5}{8}$
(c) Selected outcomes: OEE, OEO, OOO, OOE; Probability: $\frac{1}{2}$