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# How to figure the probability?

Discussion in 'Chit Chat' started by Toonces, Nov 17, 2007.

1. ### Toonces

You flip a coin 5 times. What is the probabilty that it will come up heads (not heads or tails, but heads specifically) AT LEAST twice?

(I don't know the answer; more importantly, what is the formula?)

2. ### Toonces

If I figure correctly, there are 32 possibilities (2 to the 5th power). 26 outcomes are favorable, but I'm not sure how to get the 26 without doing it manually.

3. ### u21c3f6

You are correct. The (C)ombination formula is: nCr = n!/r!(n-r)! where n = # trials and r = # to be selected.

Not sure about a shortcut but it can be solved one of two ways, how many meet your criteria or total trials minus how many do not meet your criteria.

I will use option 2 since it is shorter. How many results have 0 or only one head?

5!/0!(5-0)! + 5!/1!(5-1)! = 6 that do not have at least 2 heads or 32-6 = 26 that have at least two heads.

Joe.

4. ### rosy2

you would use the binomial distribution function and solve like ...

X = P(exatly 2) + P(exatly 3) +
P(exatly 4)+P(exatly 5)

5. ### MGJ

It is slightly less work to do it Joe's way: calculate Y = probability(less than 2 heads) and then X = (1 - Y)

Y = P(exactly 0 heads) + P(exactly 1 heads) = (1/32) + (5/32) = (6/32)

Then X = Probability(2 or more heads) = 1 - Y = (26/32)

using the good old binomial probability distribution mentioned by rosy2:
P(exactly 0) = (5 choose 0)*(p^0)*((1-p)^5) = 1*1*(1/2)^5 = 1/32
P(exactly 1) = (5 choose 1)*(p^1)*((1-p)^4) = 5*((1/2)^1)*(1/2^4) = 5/32

6. ### stock777

Now that you've posted this, Vegas will have to change all the rules.

7. ### Renegen

It's just binomial distribution dudes.

1 - (P(0) + P(1) )

Hmm nevermind, I didn't see it was there. you had to make it all complicated.

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