SOLUTION: A game of chance involves spinning a wheel that has 4 equally likely areas to land on. Red, blue, green and white. If paul plays the game 5 times, what is the probability he wins 3

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Question 547249: A game of chance involves spinning a wheel that has 4 equally likely areas to land on. Red, blue, green and white. If paul plays the game 5 times, what is the probability he wins 3 or fewer times?
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
We need to know how Paul wins to answer this question, but let's just assume he wins if it lands on red, and hopefully this helps.

Since the wheel is equally likely to land on any of the 4 areas, the probability that it lands on red is 1%2F4 (as is the probability of each of the other areas).
The probability that Paul wins 3 times is
%281%2F4%29%2A%281%2F4%29%2A%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29=9%2F1024
(Note: we are using the product rule (the "or" rule), and also note that 3%2F4 is the probability that the wheel will not land on red).
Similarly,

The probability that Paul wins 2 times is
%281%2F4%29%2A%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=27%2F1024

The probability that Paul wins 1 times is
%281%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=81%2F1024
And
The probability that Paul wins times is
%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29%2A%283%2F4%29=243%2F1024

Now the probability that Paul wins 3 or fewer times we can get by using the sum rule and adding each of these individual probabilities.
9%2F1024%2B27%2F1024%2B81%2F1024%2B243%2F1024=360%2F1024=45%2F128