Learning statisticts and probability

In summary, the conversation discusses the probability of going to a restaurant and seeing a movie on Friday night. The initial intuition is to add the probabilities and divide by 2, but it is realized that the combined chances must be less than 45%. Multiplying 45% by 75% or 75% by 45% gives a correct answer of 33.75%. The conversation also mentions the possibility of the events being independent, in which case the probabilities can just be multiplied together. Finally, it is also mentioned that if the events are certain, the probability of going to both the restaurant and the movie is 20%.
  • #1
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I saw this problem in a book review, but it doesn't give an answer

If there is a 75% chance I will go out and eat dinner at a restaurant on Friday night and there is 45% chance I will go see a movie on friday night
then what is the probability that I see a movie and eat dinner at a restaurant?

At first my stupid intuition told me to just add 75 and 45 and divide by 200
which would be 120/200 = .6 = 60% (.75+.45)/2

But then I realized that the combined chances had to be less than 45%.
So i just multiplied 45*0.75 = 33.75% or 75*.45 = 33.75%
33.75 seems correct to me although the logic is weird
is this the right answer and is there another way of finding the solution

also are there any good books you could recommend for learning statisticts and probability
 
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  • #2
Depends if you consider them to be independent events or not, otherwise knowing the probability of A and the probability of B doesn't tell you anything about the probability of A and B occurring.

If they are independent then, yes, you just multiply them together.
 
  • #3
Could we also understand : I go to the restaurant or to the movie with certainty (I cannot choose neither of them) :

p(movie or dinner)=1=p(movie)+p(diner)-p(movie and diner)

Implying : p(movie and diner)=.75+.45-1=.2=20% ??
 
  • #4
Yes, that's fine. The events are not independent in that case.
 

FAQ: Learning statisticts and probability

What is the difference between statistics and probability?

Statistics is the study of data and how to collect, analyze, and interpret it. Probability is the branch of mathematics that deals with the likelihood of events occurring.

Why is learning statistics and probability important?

Statistics and probability are essential for making informed decisions based on data in various fields such as science, economics, and business. It helps us understand and make predictions about the world around us.

What are some common applications of statistics and probability?

Some common applications of statistics and probability include risk assessment, market research, medical studies, and quality control in manufacturing.

How can I improve my understanding of statistics and probability?

To improve your understanding of statistics and probability, it is important to practice solving problems and interpreting data. Taking courses, reading textbooks, and attending workshops can also be helpful.

Can statistics and probability be used to manipulate data?

No, statistics and probability are used to analyze and interpret data objectively. However, it is important to be cautious of how data is collected and presented, as it can be manipulated to support a certain conclusion.

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