Answer
a) 6; .46
b) 101; .3936
c) Roulette game
Work Step by Step
a) He is betting 5 dollars each time, so for each win, he gets: $5\times35=175$ dollars. He bets 1000 dollars, so he needs $\frac{1000}{175}\approx 6$ wins.
We find that the probability that he will make a profit is:
$.5 \times \frac{\frac{1}{38}}{\frac{1}{35}}=.46$
b) To make a profit, he must win on over half of his bets, so he must win 101 hands.
a. We find:
$\mu=np=(200)(.492)=98.58$
$ \sigma=\sqrt{npq}=\sqrt{(200)(.492)(.507)}=7.07$
Thus, we find z:
$z=\frac{100.5-98.58}{7.07}=.6064$
Thus, using the table of z-scores, we find that this corresponds to a probability of $1-.6064=.3936$
c) The roulette game has a higher chance of making a profit, so it is the better option.
