Question 1038847: By tossing an unfair coin, how can we get probability 1/2? I believe one scheme would be to toss the coin 2 times and keep only the HT or TH outcomes and disregard the TT or HH. What if we wanted the probability to be 1/3 or 1/5?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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