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 in the table below. note that each outcome has the same probability.
for 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.
event a: two or more even numbers
event b: an odd number on each of the first two rolls
event c: an even number on the last roll or the second roll (or both)

Explanation:

Step1: Analyze Event A (Two or more even numbers)

For an outcome to be in Event A, it must have 2 or 3 even numbers.

• For EEE: all three are even.
• For EEO: first two are even.
• For EOE: first and third are even.
• For OEE: second and third are even.

Step2: Analyze Event B (An odd number on each of the first two rolls)

For an outcome to be in Event B, the first two characters must be 'O'.

• For OOE: first two are odd.
• For OOO: first two are odd.

Step3: Analyze Event C (An even number on the last roll or the second roll (or both))

For an outcome to be in Event C, the second or the third character (or both) must be 'E'.

• For OEO: second is 'E'.
• For EEE: second and third are 'E'.
• For EEO: second and third are 'E'.
• For OOE: third is 'E'.
• For OEE: second and third are 'E'.
• For EOO: second is 'E'.
• For EOE: second and third are 'E'.

Answer:

Outcomes	Event A (Two or more even numbers)	Event B (An odd number on each of the first two rolls)	Event C (An even number on the last roll or the second roll (or both))
EEE	:heavy_check_mark:		:heavy_check_mark:
EEO	:heavy_check_mark:		:heavy_check_mark:
OOE		:heavy_check_mark:	:heavy_check_mark:
OEE	:heavy_check_mark:		:heavy_check_mark:
EOO			:heavy_check_mark:
OOO		:heavy_check_mark:
EOE	:heavy_check_mark:		:heavy_check_mark: