List the outcomes comprising the specified event. When a quarter is tossed four

Question

List the outcomes comprising the specified event.

When a quarter is tossed four times, 16 outcomes are possible.

HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows.

A = event exactly two tails are tossed
B = event the first and last tosses are the same

List the outcomes that comprise the event (A & B).

HHTT, HTHT, HTTH, THHT, THTH, TTHH

HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT

HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTT

HTTH, THHT

HHTT, HTHT, HTTH, THHT, THTH, TTHH

HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT

HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTT

HTTH, THHT

Explanation / Answer

A = event exactly two tails are tossed
B = event the first and last tosses are the same

A = {TTHH, THTH, THHT, HTHT, HTTH, HHTT}

B = {HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT}

A & B = {HTTH, THHT}

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