Please show all work until its put into calculator thank you

Please show all work until it\'s put into calculator thank you!

Mr. Lucky has $1000 with him. He plans to make a series of independent bets at even money at a casino. The probability of Mr. Lucky\'s winning any one bet is .49. He plans to continue until either he is $100 ahead or he loses the $1000. Mr. Lucky\'s bet will all be the same size, either $1, $5, $10, $50, or $100. Use a calculator to estimate the following:

a. For each size of bet, find the probaility that Mr. Lucky succeeds in winning the $100. Answers: .0183, .4492, .6662, .8686, .8898

b. For each size bet, how long does it take, on average, to settle the matter? Answers: 48,993, 5,058.5, 1,336.0, 44.5, 10.6

Solution

prob winning =0.49

a) betting is 1 5 10 50 100

For betting 1, prob he wins 100 = P(he wins 100 draws) = 0.49+0.51(0.49)+0.51^2(0.49)+.....

= 0.0182

b) similarly for 5 prob =0.4492

for 10 = 0.6662

Prob for 50 0.8686

Prob for 100 = 0.8898