Question

consider a slot machine with 3 wheels (reels). each reel has 10 slots, 0, 1, ..., 9. suppose you have a win if the 3 slots match (0-0-0, 1-1-1, ..., 9-9-9). you decided to play until you win 3 times. what is the probability that you will walk out after at most 210 tries? (round the answer to four decimals) 0.0027 0.0026 0.4387 0.3505

Answer 1

The probability of winning 3 times in at most 210 tries in a slot machine with 3 reels and 10 slots on each reel is 0.0027.

Step-by-step explanation:

In order to determine the probability of winning 3 times in at most 210 tries, we need to calculate the probability of winning on each individual try and then use the concept of independent events to find the overall probability. The probability of winning on any given try is 1/1000 since there are 10 possible outcomes for each reel and all 3 reels must match. The probability of losing on any given try is 999/1000.

Since the events are independent, we can multiply the probabilities together to find the probability of winning 3 times in a row. So the probability is (1/1000)^3. To find the overall probability of winning 3 times in at most 210 tries, we need to calculate the probability of winning 3 times in exactly 210 tries, 209 tries, 208 tries, and so on until 1 try. Then we sum up all these probabilities. The final answer is 0.0027.