Question

a 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: exactly one odd number
select all outcomes that are contained in event a.
□ oeo □ eeo □ ooe □ eoe □ eee □ oee □ eoo □ ooo
find the probability of event a.
probability:□
(b) event b: no even numbers on the last two rolls
select all outcomes that are contained in event b.
□ oeo □ eeo □ ooe □ eoe □ eee □ oee □ eoo □ ooo
find the probability of event b.
probability:□
(c) event c: an even number on both the first and the last rolls
select all outcomes that are contained in event c.
□ oeo □ eeo □ ooe □ eoe □ eee □ oee □ eoo □ ooo
find the probability of event c.
probability:□

Explanation:

(a) Step1: Identify outcomes with exactly one odd

Outcomes: EEO (1 odd), OEE (1 odd), EOE (1 odd) → 3 outcomes

(a) Step2: Calculate probability

Total outcomes = 8 → Probability = $\frac{3}{8}$

(b) Step1: Identify outcomes with no even last two rolls

Last two rolls odd: OOO (last two O), EOO (last two O) → 2 outcomes

(b) Step2: Calculate probability

Probability = $\frac{2}{8} = \frac{1}{4}$

(c) Step1: Identify outcomes with even first and last rolls

First=E, last=E: EEO (E,E), EOE (E,E), EEE (E,E) → 3 outcomes

(c) Step2: Calculate probability

Probability = $\frac{3}{8}$

Answer:

(a) Selected outcomes: EEO, OEE, EOE; Probability: $\frac{3}{8}$
(b) Selected outcomes: OOO, EOO; Probability: $\frac{2}{8} = \frac{1}{4}$
(c) Selected outcomes: EEO, EOE, EEE; Probability: $\frac{3}{8}$