Please show all work full solutions Thank you Mr Lucky has 1

Please show all work, full solutions! 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

Size is 1.

For having 100 ahead = winning 1100 = 1100(0.49)= 539

For losing 1000 = 1000(0.49) = 490

Hence answers will be

for 1 48993,

for 5 it is 5058.5

for 10 it is1336

for 50, 44.5

for 100, 10.6

Problem