Okay so I am designing a probability game involving three spinners called "WordWheel."
There are a few simple rules for the game:
- There will be 3 spinners that will each have different letters on them. The first spinner will have B,T,A,E,S. The middle spinner will have A,E,I,O,U.The last spinner will have M,R,Y,D,J.
- The whole point in this game is to get an actual three letter word.
- Before you spin, you have to bet a value of tokens (you start off with 5) on getting a word with a specific letter in it.
- Once all three have been spun, if you don’t get a word with that letter, you loose the bet.
Now, I already know that there is a total of 125 different outcomes using a tree diagram. I have also looked into which of those are ACTUAL words, which ends up in 20. The only ones I actually classified as real words is: Bay, Bad, Boy, Bud, Bar, Bam, Bed, Bid, Bum, Toy, Tad, Tar, Air, Aim, Aid, Ear, Sod, Sum, Sad, Say. (and I would like to keep it this way, makes it easier for me!)
So I figured it would be P(win)= 20/125
But I also have to incorporate the bet with a specific letter in it. So I thought I should find how many times each letter occurs out of the 20 words, shown below.
P(B)= 9/20 , P(T)= 3/2 , P(A)= 12/20 , P(E= 2/20 , P(S)= 4/20 , P(I)= 4/20 P(O)= 3/20 , P(U= 3/20 , P(J)= 0/20 , P(D)= 8/20 , P(Y)= 3/20 , P(R)= 4/20 P(M)= 4/20
I just don't know what to do with these to find out the final probability of winning.
Those are just my ideas, so I do realize I may not be on the right track but if I am wrong please correct me and help me to get in the right direction. I'm really hoping this game works.