daretodream wrote:The probability is 1/2 that a coin will turn out to be tails on any given toss. A coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses.
In such questions ,it is important to note that in any case the probability will be (1/2) only.[whether it is heads or tails]
So as a shortcut approach many a times you will find that the answer is
(1/2)^x (where x is the no. of the tosses.)
Now, over here we are talking about
consecutive tosses ,so we also have to consider the selections of the order of those tails.
Hence,Answer will be
[(1/2)^x]*(No. of arrangements)
Case 1:-All Heads.Only 1 selection.
Case 2:-4 consecutive Heads and tail.(The posn. of tail can be selected in 2 ways)
Case 3:-Three consecutive heads and two tails(the 2 tails can be selected in 3 ways).
Hence,the [spoiler]answer will be [(1/2)^x]*(No. of arrangements) = [(1/2)^5]*(6)
=6/32 =3/16[/spoiler]
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