MHB What is the probability that he is having pizza?

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The discussion centers on calculating the probability that Homer is having pizza given that he is watching Monday Night Football. The provided probabilities are 0.6 for watching football, 0.45 for having pizza, and 0.25 for doing both. A participant expresses confusion about why the probability of doing both is not simply the product of the two individual probabilities. Clarification is offered that the 0.25 is a given value, not derived from multiplying the other probabilities, and a visual aid with overlapping circles is suggested to better understand the relationships. The correct probability that Homer is having pizza while watching football is ultimately calculated as 5/12.
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Hi! So I am confused with this problem:

Homer watches Monday Night Football with a probability .6, he has pizza on Monday night with a probability .45, and he does both with probability .25. When you call him on Monday night, you learn that he is watching Monday Night Football. What is the probability that he is having pizza?

The answer is 5/12, I don't understand why :(

First of all, I do not understand how the probability of doing both is .25. Should it not be .6*.45? So, the formula should be for Probability of having pizza given that he is watching MNF, which would be: (.6*.45)/(.6*.45)+(.45*.4)... but I am obviously doing something wrong... :(
 
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navi said:
Hi! So I am confused with this problem:

Homer watches Monday Night Football with a probability .6, he has pizza on Monday night with a probability .45, and he does both with probability .25. When you call him on Monday night, you learn that he is watching Monday Night Football. What is the probability that he is having pizza?

The answer is 5/12, I don't understand why :(

First of all, I do not understand how the probability of doing both is .25. Should it not be .6*.45? So, the formula should be for Probability of having pizza given that he is watching MNF, which would be: (.6*.45)/(.6*.45)+(.45*.4)... but I am obviously doing something wrong... :(

.25 is not calculated from .6 and .45. It is given.

Draw two separate circles.

Label one "p( Football ) = 0.60"
Label the other "p( Pizza ) = 0.45"
Now, slide them together until they overlap.
--- Label the overlap "p(Both) = 0.25".
--- Put 0.60 - 0.25 = 0.35 in the football lune
--- Put 0.45 - 0.25 = 0.20 in the pizza lune

If you have the picture right, you should be able to answer the questions.

Are there more weird icons that can be developed from simple words? ( P i z z a ) gives (Pizza).
 
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