Question

A roulette wheel contains the integers 1 through 36, 0, and 00. suppose that you spin the wheel 6 times and that each time you bet on a single number. what is the probability (rounded to the nearest hundredth) that you win on at least one bet?

Answer 1

The probabability of winning on at least 1 bet is equal to 1 less the probaility of not winning on either of the 6 bets.

The probability of not wining on any bet is independent of winning or not winning on any of the bets, so the combined probability is calculated as the product of each individual probability.

Each indivitual probability of not winning the is:

(number of not winning outcomes) / (number of possible outcomes) = 37 / 38.

Then, the combined probability of not winning the six times is: (1/38)*(37/38)*(37/38)*(37/38)*(37/38)*(37/38) =(37/38)^6

Therefore, the probability of winning at least one bet is:

= 1 - (37/38)^6 ≈ 1 - 0.973684 ≈ 0.03.

Answer: 0.03.