Question

Each time you click a toggle switch, the switch either turns from off to on or from on to off. Suppose that you start with three toggle switches with one of them on and two of them off. On each move you randomly select one of the
three switches and click it. Let m and n be relatively prime positive integers so that m/n is the probability that after four such clicks, one switch will be on and two of them will be off. Find m + n.

Answer 1

help plz?? anyone?

Answer 2

um is the 3 switch

Answer 3

Hold on I think I can get you an answer.

Answer 4

lol its 3d switch

Answer 5

There are 3 options to choose from so start with 3
There are 4 times you may try this
Times 3 four times 3*3*3*3
This equals 27
With only one possible way to get it to one on two off, you are left with 1/27

Answer 6

Make sense?

Answer 7

this is not the right answer..

Answer 8

\[{2+2+1+2+1 \over 5+4+3+2+1}= {8 \over 15}\]
m+n= 8+15 =23

how about 23?

Answer 9

neither.. :S

Answer 10

sorry, this should be right:
let the total number of outcomes be 3^4=81
eg. with 3 switches X,B,C we would have XXXX, XXXB, XBXX, XCXX, BCCB... etc

\[\frac mn ={10+32+12+8+1 \over 16 +32+24+8+1}= \frac{63}{81}=\Large\frac 79\]

m+n=15

Answer 11

**m+n=16