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?
The probability of a cherry on each of the two wheels = 1/20, while the middle wheel = 9/20.
The probability of all events occurring is found by multiplying the probability of the individual events.
To calculate the probability of winning the jackpot in this scenario, we need to determine the probability of getting cherries on each of the three wheels and then multiply those probabilities together.
Let's start with the middle wheel. Since there are 9 cherries out of 20 symbols on that wheel, the probability of getting a cherry on the middle wheel is 9/20.
Now, let's consider the left and right wheels. Each of them has one cherry out of 20 symbols. So the probability of getting a cherry on each of those wheels is 1/20.
To calculate the probability of all three events happening simultaneously (i.e., winning the jackpot), we multiply the individual probabilities together:
Probability of winning the jackpot = (Probability of cherry on middle wheel) * (Probability of cherry on left wheel) * (Probability of cherry on right wheel)
= (9/20) * (1/20) * (1/20)
= 9/8000
Therefore, the probability of winning the jackpot in this scenario is 9/8000.