Answer:
Part a: The probability of breaking even in 6 tosses is 0.3125.
Part b: The probability that one payer wins all the money after the 10th toss is 0.0264.
Explanation:
Part a
P(success)=1/2=0.5
P(Failure)=1/2=0.5
Now for the break-even at the sixth toss
P(Break Even)=P(3 success out of 6)
P(3 success out of 6)
So the probability of breaking even in 6 tosses is 0.3125.
Part b:
So the probability that one of the player wins all the money after the 10th toss is given as the tenth toss is given as a win so
Wins in 9 tosses is given as 9!/7!=72
The probability that the other person wins
Wins in 8 out of 10 tosses is given as 10!/8!(10-8)!=10!/8!2!=45
So the probability of all the money is won by one of the gambler after the 10th toss is given as
P=number of wins in 9 tosses-Number of wins in 10 tosses/total number of tosses
P=(72-45)/2^16
P=0.0264
So the probability that one payer wins all the money after the 10th toss is 0.0264.