Question

Consider the biased coin that produces head 70% of the time from the probability calculation in week 2. One tosses the coin twice. Conditioning on that we know both tosses have the same outcome, what is the probability of that both tosses are tails?

1- 0.09

2- 0.125

3- 0.155

4- 0.5

Answer 1

We’re told (a) that the coin is biased 70% heads and 30% tails and (b) that both tosses have the same outcome: i.e. they are both heads or both tails.

Assuming the tosses are independent of one another, the probability of getting two heads is (.7)*(.7)=0.49.

The probability of getting two tails is

(.3)*(.3)=0.09.

As the question says, the total probability of getting two of the same outcome is the sum of these or 0.49+0.09=0.58.

since the two outcomes being studied are mutually exclusive of these ,

0.49/0.58=0.844

And are two heads and

0.09/0.58=0.1552 is two tailes.

Therefore, answer is

3)0.155