Suppose a weighted coin is repeatedly tossed until a heads appears for the first time at which point the experiment stops. On each flip, the probability of a heads is 0.25. Assuming that the tosses of the coin are independent of each other, find the probability that more than three flips are needed to get our first heads
Let E = {more than three flips are needed to get our first heads}
Let Ei = {we obtain our first heads on flip i}

A) Express E in terms of Ei

B) express E4 in terms of Hi and Ti where Hi = {heads on flip i} and Ti = {Tails on flip i}. Express P(E4) **keeping in mind P(Hi) = .25 and P(Ti)= .75)

C) Express E5 in terms of Hi and Ti, and find P(E5)

D) Express E6 in terms of Hi and Ti, and find P(E6)

E) Now find P(E)