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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)

Verified Answer :

kotime1

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

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).

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