What is the probability that he is having pizza?

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In summary, the conversation discusses the probabilities of Homer watching Monday Night Football and having pizza on Monday night, with a probability of .6 and .45 respectively. It is also mentioned that there is a probability of .25 that he does both. When it is revealed that he is watching Monday Night Football, the conversation then questions the probability of him having pizza. The solution is determined to be 5/12, but there is confusion about the calculation of the probability of doing both. The proper calculation involves subtracting the overlap of the two events and placing the remaining probabilities in their respective circles. The conversation ends with a question about the possibility of developing more icons from simple words.
  • #1
navi
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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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  • #2
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).
 

FAQ: What is the probability that he is having pizza?

What is the definition of probability?

Probability is a measure of the likelihood of a specific event occurring. It is usually represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be expressed as a fraction, decimal, or percentage.

What factors influence the probability of someone having pizza?

The probability of someone having pizza can be influenced by various factors such as their personal preferences, availability of pizza, cultural norms, and social influences. It can also be affected by factors like time of day, location, and cost.

Can probability be used to predict the future?

No, probability cannot be used to predict the future with certainty. It is a measure of likelihood based on past events and cannot account for unforeseen circumstances or randomness.

Is it possible to have a probability of 1?

Yes, a probability of 1 means that the event is certain to occur. This means that the outcome is guaranteed and will happen every time. However, in real-life situations, it is rare to have a probability of 1 as there is always a chance for unexpected events to occur.

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