Probability of 3 Heads and 2 Tails in 5 Coin Tosses

[ilovehkng]

A fair coin is tossed five times. What is the probability of obtaining three heads and two tails?

I cannot find out the right answer by my way

Ans: 5/16

Thanks :)

 

[statdad]

Since there are only two possibilities for each flip (head or tail), if you find the probability of having exactly 3 heads you've got the question answered. what distribution do you know of that

- deals with counts of a particular outcome
- assumes only two possible outcomes per trial
- assumes that successive trials are independent

 

[paulfr]

Yes the Bernoulli Trial formula will directly yield the answer for n=5, p=0.5 and k=3.

Another way is this.
Total possible outcomes is 2^5=32
How can you Permute [arrange] 5 items, 5 at a time, with 3 the same and 2 the same ?
5 ! / [ (5-5)! 3! 2! = 10
10/32 = 5/16