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A magician designed an unfair coin so that the probability of getting a Head on a flip is 60%. If he flips the coin three times, what is the probability that he flips more Heads than Tails? Express your answer as a common fraction.

Guest Aug 2, 2017
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"More heads than tails"   means these possibilities  :

 

2 Heads -  1 Tail

3 Heads - 0 Tails

 

Probability of  2 Heads - 1 Tail  =    C(3,2) (.60)^2 (.40)   =  3 * (.36)(.40)  =  3 * .144  =   3 (144/1000)  =  3 ( 18/125)  =

54/125

 

Probability of 3 Heads = (.60)^3  =  .6 (.36) = .216  = 216 / 1000  =  27 / 125

 

So....the total probability  =   54 / 125  +  27 / 125  =   81 / 125

 

 

cool cool cool

CPhill  Aug 2, 2017

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