Baye's Rules Help: Probability of Picking a 1-Sided Coin

[wown]

Question:
You have 100 coins. 99 are fair and 1 is double sided. You pick a random coin and flip it 10 times and get 10 heads in a row. What is the probability that you picked the double sided coin?

Response / help needed:
Probablity of picking a 1 sided coin = .01
Probability of heads 10 times in a row with an fair coin = .5^(10)
Probability of heads 10 times in a row with an unfair coin (assuming the head is on both sides) = 1

So, i think, according to baye's, the equation should be
.01*1/ (.01*1+ .5^10*.99) = .912

Is that correct?

Also, what would you do if you do not assume heads is on both sides?

 

[D H]

So, i think, according to baye's, the equation should be
.01*1/ (.01*1+ .5^10*.99) = .912

Is that correct?

Looks good!

Also, what would you do if you do not assume heads is on both sides?

You would calculate P(fair coin | 10 heads in a row), which would give the same denominator as you had but the numerator would be 0.99*0.5¹⁰. Taking 1 minus this value will yield the same result you obtained.