Answer
a) 6; 0.46
b) 101; 0.3936
c) Neither game
Work Step by Step
a)He is betting $5$ dollars each time, so for each win, he gets $5\cdot35=175$ dollars. He bets $1000$ dollars, so he needs $\frac{1000}{175}≈6$ wins.
We find that the probability that he will make a profit is:
$0.5\cdot\frac{\frac{1}{38}}{\frac{1}{35}}=0.46$
b) We find:
$μ=np=(200)(0.492)=98.58$
$σ=\sqrt{npq}=\sqrt{(200)(0.492)(0.507)}=7.07$
Hence, we find z:
$z=\frac{100.5−98.58}{7.07}=0.6064$
Thus, using the table of z-scores, we can find that the corresponding probability is: $1−0.6064=0.3936 $.
c) The roulette game has a higher chance of making a profit, so it is the better option. However, he should choose t play neither.
