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# I'd like a different way to solve it

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Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that at least 15¢ worth of coins come up heads?

I solved it (answer = 5/8) using brute force (E.g. listing out all the combinations) but I feel there must be some more efficient way to solve it. What could it be? Thanks in advance :D

Edit: Changed "brute fort" to "brute force" :)

May 1, 2020
edited by CentsLord  May 1, 2020

#1
+1

I agree the only way I know how to do it is brute force, similarly I think CPhill answered this question with the same techqnie as you...

By the way everything below this is 100% CPhill's work even though I used the same methord

16 possible outcomes

P         N           D           Q                     Value  of Heads

H        H           H           H                        .41

T        H           H           H                        .40

T        T           H            H                        .35

T        T           T            H                        .25

T        T           T           T                            0

H       T            T           T                         .01

H       H           T            T                        .06

H      H            H            T                        .16

T       H           T            T                         .05

T      T            H            T                         .10

H      T            T            H                         .26

T      H           H             T                         .15

T      H           T             H                         .30

H     T            H            T                          .11

H     T            H            H                          .36

H     H           T             H                          .31

P ( 15 cents or more of heads)  = 10/16 =  5/8

May 1, 2020
#2
+1

Agreed, but is there a more efficient way? o _ O

CentsLord  May 1, 2020
#3
+1

The probability is:
4!/(2!.2!.2^4) + 4!/(3!.2^4) =3/8 + 1/4 = 5 / 8

Guest May 1, 2020
#4
+3

Thank you so much! I can try and understand some of what you wrote, but why did those numbers get there? Could you explain more? :D

CentsLord  May 2, 2020