Question

Jack is playing a game where he flips a coin and rolls a number cube labeled 1 through 6. He listed the possible outcomes in the sample space shown below.

{(H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Which two elements did he leave out by mistake?

(H, 1) and (T, 6)
(H, 6) and (T, 1)
(H, 2) and (T, 6)
(T, 1) and (T, 6)

Answer 1

The answer is (H, 1) and (T, 6)

Answer 2

Answer: The correct option is (A) (H, 1) and (T, 6).

Step-by-step explanation: Given that Jack is playing a game where he flips a coin and rolls a number cube labeled 1 through 6.

Jack listed the possible outcomes in the sample space 'S'' as follows:

S' = {(H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

We are given to select the correct option that contains the two elements Jack left out by mistake.

The sample space for the event of flipping a coin is {H, T}

and

the sample space for the event of rolling a number cube labeled 1 through 6 is {1, 2, 3, 4, 5, 6}.

Let, 'S' represents the actual sample space for the event.

Then, we get

S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}.

Comparing S with S', the two missing elements were (H, 1) and (T, 6).

Thus, the correct option is (A).