slot machines are now video games, with outcomes determined by random number generations. in the old days, slot machines were like this: you pull the lever to spin 3 wheels; each wheel has 20 symbols, all equally likely to show when the wheel stops spinning; the three wheels are independent of each other. suppose the middle wheel has 9 cherries among its 20 symbols, an the left and right wheels have one cherry each.
you win the jackpot if all three wheels show cherries. what is the probabiity of winning the jackpot?
To find the probability of winning the jackpot on a slot machine with the given specifications, we need to determine the probability of getting a cherry on each wheel and then multiply them together.
Let's break it down step by step:
1. Probability of getting a cherry on the middle wheel:
Out of the 20 symbols on the middle wheel, 9 are cherries. Thus, the probability of landing a cherry on the middle wheel is 9/20.
2. Probability of getting a cherry on the left and right wheels:
Since each of the left and right wheels has only one cherry among its 20 symbols, the probability of landing a cherry on either the left or right wheel is 1/20 for each.
3. Since the three wheels are independent, we can multiply the probabilities from steps 1 and 2 to find the probability of winning the jackpot:
Probability of winning = Probability of cherry on middle wheel * Probability of cherry on left wheel * Probability of cherry on right wheel
Probability of winning = (9/20) * (1/20) * (1/20) = 9/8000
Therefore, the probability of winning the jackpot on this particular slot machine is 9/8000.