a number cube is rolled three times. an outcome is represented by a string of the sort oee (meaning an odd…

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 in the table below. note that each outcome has the same probability.\nfor each of the three events in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event.\n\n| | outcomes | probability |\n|----|----|----|----|----|----|----|----|----|----|\n| event a: alternating odd number and even number (with either coming first) | oee | ooo | eoo | eee | foe | oeo | ooe | eeo | |\n| event b: an even number on both the first and the last rolls | | | | | | | | | |\n| event c: no odd numbers on the last two rolls | | | | | | | | | |

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 in the table below. note that each outcome has the same probability.\nfor each of the three events in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event.\n\n| | outcomes | probability |\n|----|----|----|----|----|----|----|----|----|----|\n| event a: alternating odd number and even number (with either coming first) | oee | ooo | eoo | eee | foe | oeo | ooe | eeo | |\n| event b: an even number on both the first and the last rolls | | | | | | | | | |\n| event c: no odd numbers on the last two rolls | | | | | | | | | |

Answer

Explanation:

Step1: Identify outcomes for Event A

Outcomes with alternating odd - even are OEO and EOE.

Step2: Calculate probability for Event A

There are 8 total outcomes. Probability = $\frac{2}{8}=\frac{1}{4}$.

Step3: Identify outcomes for Event B

Outcomes with even on first and last are EEE and EEO.

Step4: Calculate probability for Event B

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

Step5: Identify outcomes for Event C

Outcomes with no odd on last two are OEE, EEE, EEO.

Step6: Calculate probability for Event C

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

Answer:

Event Outcomes Probability
Event A OEO, EOE $\frac{1}{4}$
Event B EEE, EEO $\frac{1}{4}$
Event C OEE, EEE, EEO $\frac{3}{8}$