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by CITI29 » Sun Jul 20, 2008 8:26 am
Q--If the coin is tossed 5 times, what is the probability that at least 3 out of 5 times it will show heads?

pls explain as why ans is '1/2'...isn't probability of getting heads is same as getting tails?
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by pepeprepa » Sun Jul 20, 2008 9:47 am
You have 2^5 total number of possibilities: 32

We look for the number of combinations in which we have either 3 heads, or 4 heads, or 5 heads.
(5 3) it gives 10 possibilities
(5 4) it gives 5 possibilities
(5 5) only one possibility: HHHHH

So 16/32=1/2

Hope it helps.
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by Stuart@KaplanGMAT » Sun Jul 20, 2008 10:25 am
pepeprepa wrote:You have 2^5 total number of possibilities: 32

We look for the number of combinations in which we have either 3 heads, or 4 heads, or 5 heads.
(5 3) it gives 10 possibilities
(5 4) it gives 5 possibilities
(5 5) only one possibility: HHHHH

So 16/32=1/2

Hope it helps.
Great solution!

We can also look at this from a common sense point of view:

We know that coin flips are random and follow a symmetrical distribution (i.e. the chance of getting all heads = the chance of getting no heads).

We know that if we flip a coin 5 times, there are 6 possibilities:

0H, 1H, 2H, 3H, 4H and 5H

This question asks for the prob of 3H, 4H or 5H. Since the distribution is symmetrical, that will be the exact same as the prob of 2H, 1H or 0H (since P(0H) = P(5H), P(1H) = P(4H) and P(2H) = P(3H)). Therefore, there's a 50% chance of getting what we want.
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