In: Statistics and Probability
LEt p be the event of getting a tail.
If the out come T appears b times in a row peter will get all
the money john has .The probability of this event is
Suppose if a Head appears in between then john will have b+1
dollars( This one dollar is obtained from the peter for the head
obtained) . so to get all the money john has T should happen b+1
times, The probability of this event is probability of getting a
head in b+2 tosses of a coin=
Now suppose there are two heads occurred before you get b tails.
The john will have b+2 dollars. The two more tails will have to
happen to take all the money from john . Total number of tosses
required for this event is (b+2 )tails+2 heads. The probability of
this event is the probability of getting two heads in b+4 tosses=
Similarly if we proceed we get the probability of n heads in b+n
tosses =
There fore the Probability that peter wins all the money from
john =