Ghhhhhh
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Hhhh
HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT
HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT.
Each flip has two possible outcomes and they are independent events, so there are 24 = 16 possible results. Of these, only 2 (HHHH, TTTT) are the same 4 each time, Thus: probability = 2/16 = 1/8
There are 16 permutations of a coin tossed 4 times. They are ...HHHH - HHHT - HHTH - HHTTHTHH - HTHT - HTTH - HTTTTHHH - THHT - THTH - THTTTTHH - TTHT - TTTH - TTTT... and the permutations with only one tail are bolded. There are 4, so the probability of flipping a coin 4 times and getting only 1 tail is 4 in 16, or 1 in 4, or 0.25.The coin does not have a memory therefore the probability is always 50/50.