Supposed a certain game is fair and costs $4 if you lose and has a net payoff of $9 if you win. The only possible outcomes of the game are winning and losing.
What is the probability of winning?

32.5% Win Rate

Step-by-step explanation:

I got this answer by first:

( 9 ) * x + ( -4 ) * ( 1 - x ) = 0

9x - 4 + 4x = 0

13x = 4

then finally:

13/4 = 3.25 | And to get that into percent you multiply that by 10, giving you a 32.5% win rate. or 325 / 1000. Meaning you will win 325 out of 1000 games you play. Hope this helped!

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752