Solve the problem.
-In a game of roulette, Jorge places 170 bets of $1 each on the number 3. A win pays off with odds 35:1 and on any one spin there is a $$1 / 38$$ probability that 3 will be the winning number. Among the 170 bets, what is the
Minimum number of wins needed for Jorge to make a profit? Estimate the probability that Jorge will make a
Profit.
A) 6; 0.3121
B) 5: 0.4013
C) 6; 0.2327
D) 5; 0.496

Question

Quizplus · Accepted Answer

To find the minimum number of wins needed for Jorge to make a profit, we use the formula:

Expected Value = (Payout on Win)*(Probability of Win) - (Amount Bet)

In this case, the expected value is:

(35:1)*(1/38) - 1 = -0.0526

This means that, on average, Jorge can expect to lose $0.0526 for every $1 bet he makes on 3.

To make a profit on his 170 bets of $1 each, Jorge needs to have a total payout of at least $170. This means he needs to win:

170*(35/1) = 5950

However, since the probability of winning any single bet is only 1/38, the probability of winning 5950/35 = 170 bets is very small. We can use the binomial distribution to estimate this probability:

P(X >= 170) = 1 - binomcdf(170, 1/38, 169)

This probability turns out to be approximately 0.496, so the answer is D: 5; 0.496

Solve the Problem 1/381 / 381/38 Probability That 3 Will Be the Winning Number

Solve the Problem $1 / 38$ Probability That 3 Will Be the Winning Number