When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?
Out of 6 tosses, exactly 3 heads implies exactly 3 tails.
You can get 3 heads and 3 tails in various ways: HHHTTT, HHTHTT, TTTHHH etc
How many such ways are there? We just need to find the number of ways of arranging 3 Hs and 3 Ts in a row. This can be done in 6!/3!*3! = 20 ways (the 3 Hs are identical and the 3 Ts are identical)
Probability of obtaining HHHTTT = (0.5)*(0.5)*(0.5)*(0.5)*(0.5)*(0.5)
Probability of obtaining 3Hs and 3 Ts in any order = (0.5)^6 * 20 = 5/16
Check out this post for a discussion on binomial probability concept:http://www.veritasprep.com/blog/2012/02 ... obability/
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