Answer: P = 0.2
Step-by-step explanation:
let us define the expectations as;
Eнтн = no of flips to obtain HTH
Eн,тн = no of flips to obtain HTH where H is flipped
Eнт,н = no of flips to obtain HTH where HT is flipped
so let P and q represent the success and failure of probabilities
this gives;
Eнтн = 2 + P²Eн,тн + PqEнт,н + PqEн,тн + q²Eнтн
Eн,тн = 1 + PEн,тн + qEнт,н
Eн,тн = (1 + qEнт,н) / q
Eнт,н = 1 + p*0 + qEнтн = 1 + qEнтн
from this expression we have that;
Eнтн = (2 +(P² +Pq) (1/q + 1) +Pq) / (1-qP² + 2Pq² + q²)
E(x) = 1/P + 1/P²q
= 36.25
therefore the probability is P = 0.2
P = 0.2
