Question

) Ben and Allison each decide to wager 1 unit against the other person on flips
of an unfair coin, with probability 0.6 of landing head, until one of them runs out of money.
When the flip lands on head, Ben wins 1 unit from Allison; and when the coin lands on tail,
Allison wins 1 from Ben. At the start of the contest, Ben has 30 units and Allison has 45
units. Find
(a) the average number of flips needed until Ben is eventually broke,
(b) the average number of flips needed until Allison is eventually broke, and
(c) the average number of flips needed until either Ben or Allison is eventually broke.

Answer 1

Answer:-

Given that:-

Ben and Allison each decide to wager 1 unit against the other person on flipsof an unfair coin, with probability 0.6 of landing head, until one of them runs out of money.When the flip lands on head, Ben wins 1 unit from Allison; and when the coin lands on tail,Allison wins 1 from Ben. At the start of the contest, Ben has 30 units and Allison has 45units. Find
(a) the average number of flips needed until Ben is eventually broke,?

Let X be the number of toss required to broke Bon.

So, X take minimum 30 and probability wining of Bon from a single trial is 0.4.

So,

So,

(b) the average number of flips needed until Allison is eventually broke, and?

Similarly To Broke Alice required atleast 45 trials and probability of wining is 0.6

So, Here, Y # toss required to broke

(c) the average number of flips needed until either Ben or Allison is eventually broke.?

Either Bon or Alice will broke is