Question 1038847
you would use odds in favor to change the probability.


suppose the probability is 3/4 and you want it to be 1/2.


if the probability is 3/4,then the odds in favor is 3/1.


if the probability is 1/2, then the odds in favor is 1/1.


you want to go from odds in favor of 3/1 to odds in favor of 1/2.


let x be the factor that you need to make the adjustment.


3/1 * x = 1/1.


multiply both sides of this equation by 1/3 to get x = 1/1 * 1/3 = 1/3.


your adjustment factor is 1/3.


this means the number of heads is multiplied by 1 and the number of tails is multiplied by 3.


that will give you the fair coin results.


for example:


you toss the coin 1200 times.
heads lands 3/4 of the time and tails lands 1/4 of the time.
you get 900 heads and 300 tails.
multiply the number of heads by 1 and the number of tails by 3 and you get 900 heads and 900 tails.


now suppose the probability of getting a heads is 1/2 and you want the probability to be 1/3.


if the probability is 1/2, then the odds in favor are 1/1.


if the probability is 1/3, then the odds in favor are 1/2.


let x equal the conversion factor.


formula becomes 1/1 * x = 1/2.


multiply both sides of this equation by 1/1 to get x = 1/2 * 1/1 = 1/2.


you would multiply the number of heads by 1 and the number of tails by 2.


suppose you tossed the coin 1200 times.
you would get 600 heads and 600 tails.
multiply the number of heads by 1 and the number of tails by 2 and you get 600 heads and 1200 tails.
the probability of getting a heads is now 1/3 rather than 1/2.
the odds of getting a heads is now 1/2 rather than 1/1.


now suppose the probability of getting a heads is 3/4 and you want to make it 1/3?


if the probability of getting a heads is 3/4, then the odds of getting a heads is 3/1.


if the probability of getting a heads is 1/3, then the odds of getting a heads is 1/2.


you want to convert the odds of 3/1 to 1/2.


let x be the conversion factor.


you get 3/1 * x = 1/2


multiply both sides of this equation by 1/3 to get x = 1/6.


you would multiply the number of heads by 1 and the number of tails by 6.


assume 1200 tosses.
3/4 * 1200 = 900 heads and 300 tails.
multiply the number of heads by 1 and the number of tails by 6 and you get 900 heads and 1800 tails.
the ratio of heads to tails is now 1/2 and the probability of heads is now 1/3.


i think this is what you are looking for.


you can't change the coins so you change the counting method.