Question

Please Help!
If a coin is flipped 10 times, what is the probability that it will show all heads or all tails?



1

2



1

512



1

1,022



1

1,024



1

2,048

Answer 1

i think one half

Answer 2

1/2 i believe

Answer 3

1/512

Answer 4

well, based on simple probability, we know that it is 1/2 for the first flip. but for both to be the same? 1/4. We keep going like this
3rd flip - 1/8
4th flip - 1/16
5th flip - 1/32
6th - 1/64
7th - 1/128
8th - 1/256
9th - 1/512
10th - 1/1024
so for all the flips to be either heads or tails is a 1/1024 chance

Answer 5

for 10 heads, the probability=1/2^10=1/1024
for 10 tails, same, 1/1024
so 10 heads or 10 tails->1/1024+1/1024=1/512

Answer 6

@Curycoo explained it very well

Answer 7

there is a good vlogbrothers video that i think explains this exact question if you have acess to youtube, too, just search "Vlogbrothers probability" and you'll get a good explanation