Question

Step 1. Flip a fair coin. Step 2. If you got a head in step 1, flip two fair coins. If you got a tail in step 1, flip one fair coin. Given that you got only tails in step 2, what is the chance that you got tails in step 17 Round your answer to nearest.xx

Answer 1

It's binary tree is given as below:

HTT Head НТН О. НИТ HHH Coin 0.5 TH ТТ Tail

The above given tree shows the Favourable Outcomes.

Using, Conditional Probability,

P(A| B) = P(A andB)/ P(B) given B has already occurred.

Given that two tails outcome in step 2 (which are ticked)

We need to find , P(Tail in step1 | 2 tails in step 2)

= P( Tail in Step 1 and having 2 tails in step2)/ P( 2 tails in step 2 )

P( Tails in step 1 and 2 tails in step 2 ) = P(TT)

= 0.5*0.5 = 0.25

P( Tail in step 1 and 2 tails in step2 ) = 0.25

Now, P(2 tails in step2) = P( HTT) + P(TT)

= 0.5*0.25 + 0.5*0.5

= 0.125 + 0.25

= 0.375

P( 2 Tails in step 2 ) = 0.375

Thus, P(Tail in step1| 2 tails in step2) = 0.25/0.375

= 0.67

Please like the answer,Thanks!