petrifiedbutstanding wrote:
Hi,
Can you please solve this?
"If the coin is tossed 5 times, what is the probability that at least 3 out of 5 times it will show heads?"
If a coin is tossed 5 times, at each toss there are 2 possibilities H or T. So there are in all 2^5 = 32 possible outcomes e.g. HHHHH, HHTHH, HTTTH etc
Of these, we want those in which we get at least 3 heads.
So let us try and find the cases where we get 3/4/5 heads.
3 heads - we have to arrange HHHTT in as many different ways as possible e.g. HHTHT, TTHHH etc.
No of ways of arranging 5 letters 3 of which are same and 2 of which are same = 5!/3!2! = 10 ways
4 heads - Arrangements will be HHHHT, HHTHH etc
No of ways of arranging 5 letters 4 of which are same = 5!/4! = 5 ways
5 heads - there is only one such arrangement HHHHH
Hence probability of getting 3/4/5 heads = No of ways of getting 3/4/5 heads/Total no of ways = 16/32 = 1/2
Note: We don't really need to solve when we need 3/4/5 heads because we can have 0/1/2/3/4/5 heads and correspondingly 5/4/3/2/1/0 tails. Since the cases are symmetrical, half of them will have 0/1/2 heads(and 5/4/3 tails) and the other half will have 3/4/5 heads (and 2/1/0 tails)BTW, I think you need to post PS questions in the Quant - PS forum.
_________________
Karishma
Veritas Prep GMAT Instructor
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