Choose the 1st toss either of 2 ways, {heads,tails}
Choose the 2nd toss either of 2 ways, {heads,tails}
Choose the 3rd toss either of 2 ways, {heads,tails}
Choose the 4th toss either of 2 ways, {heads,tails}
Choose the 5th toss either of 2 ways, {heads,tails}
Choose the 6th toss either of 2 ways, {heads,tails}
Choose the 7th toss either of 2 ways, {heads,tails}
Choose the 8th toss either of 2 ways, {heads,tails}
Choose the 9th toss either of 2 ways, {heads,tails}
Choose the 10th toss either of 2 ways, {heads,tails}
Choose the 11th toss either of 2 ways, {heads,tails}
Choose the 12th toss either of 2 ways, {heads,tails}

That's 2×2×2×2×2×2×2×2×2×2×2×2 = 212 = 4096

Choose which toss will be the 1 head (the rest tails) in 12 ways.
So the probability is 12 ways out of 4096, or 12/4096, which reduces to 3/1024.

The complement event is that it will land tails all 12 times.

The probability of "all tails" is 1 way out of 4096 or 1/4096

So the probability of at least one head is 1 - 1/4096 or 4095/4096.



 

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