If you solve it in less than a minute then you are a genius
Level
2
A fair coin is tossed 10 times. What is the probability that two tails occur consecutively?
Give your answer correct to 5 decimal places.
The answer is 0.859375.
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1 solution
May not be the most efficient way but here goes. First consider the number of ways you can toss a fair coin 2^10 = 1024. Now consider how many of those combinations do not involve consecutive tails
These are all the ways we can avoid consecutive tails:
With no tails there is 1 way this can happen all heads. = 1
With 1 tail there are 10 ways as the tail can be anywhere. = 10
With 2 tails we can imagine tails must occupy the 9 gaps between the 8 heads. We must choose 2 gaps from 9. 9C2 = 36
Again using 3 tails with 7 heads. We must choose 3 gaps from 8. 8C3 = 56
With 4 tails. We must choose 4 gaps from 7. 7C4 = 35
With 5 tails. We must choose 5 gaps from 6. 6C5 = 6
So no.ways we can avoid consecutive tails = (1+10+36+56+35+6)/(1024) = 9/64 = 0.140625
1-(0.140625) yields answer = 0.859375