i know it's easy, but i wanna see the different approaches (shortcuts) to the following question:
4 coins are tossed, what is the prob that at least 3 will come up heads??
oa [spoiler]5/16[/spoiler]
coins
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i would like to solve it by taking that opposite. i.e. by taking the probability of not getting at least 3 heads.
Can anyone help??
Can anyone help??
The powers of two are bloody impolite!!
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is the OA ok?
I believe if we use Bionomial Theorem
we get
(4C3) [(1/2)^3][(1/2)^1]=4(1/2)^4=4/16
https://gwydir.demon.co.uk/jo/probability/info.htm
I believe if we use Bionomial Theorem
we get
(4C3) [(1/2)^3][(1/2)^1]=4(1/2)^4=4/16
https://gwydir.demon.co.uk/jo/probability/info.htm
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prob of atleast 3 coins showing head:
(prob of 3 coins head, 1 coin tail)+(prob of all coins head)
nitya34, you are missing out on another possibilty- all coins showing head.
so if you add 4C4*(1/2)^4=(1/2)^4=1/16 to the 4/16 you already have, you end up with 5/16
(prob of 3 coins head, 1 coin tail)+(prob of all coins head)
nitya34, you are missing out on another possibilty- all coins showing head.
so if you add 4C4*(1/2)^4=(1/2)^4=1/16 to the 4/16 you already have, you end up with 5/16
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prob of getting atleast 3 heads= 1- prob of not getting atleast 3 heads.tohellandback wrote:i would like to solve it by taking that opposite. i.e. by taking the probability of not getting at least 3 heads.
Can anyone help??
prob of not getting atleast 3 heads= (prob of no head)+ (prob of 1 head)+ (prob of 2 head)
=4C4*(1/2)^4+4C1*(1/2)^4+4C2*(1/2)^4
=1/16+4/16+6/16
=11/16
so prob of getting atleast 3 heads=1-11/16=5/16
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Super fast way to answer coin flip questions - use Pascal's Triangle.shibal wrote:i know it's easy, but i wanna see the different approaches (shortcuts) to the following question:
4 coins are tossed, what is the prob that at least 3 will come up heads??
oa [spoiler]5/16[/spoiler]
The n=4 row of the triangle is 1 4 6 4 1.
We want at least 3 heads, which means we add up the last two numbers of the row.. 4+1=5.. then we divide that by the sum of the row... 16.
Answer: 5/16
For more on the triangle (and other coin flip tips), take a look at https://www.beatthegmat.com/coin-flip-qu ... 17911.html
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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