Peter and John are tossing a coin. If it is a Head, then peter will give...

Peter and John are tossing a coin.

If it is a Head, then peter will give John 1dollar.

If it is a Tail, then John will give Peter 1dollar.

Suppose Peter has a dollar, John has b dollar.

Question: the probability that Peter wins all the money from John.

Solutions

Expert Solution

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 =

orchestra answered 1 year ago

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