Calculating the probability of an event

  • Thread starter DODGEVIPER13
  • Start date
  • Tags
    Probability
In summary: In order to find the probability of winning all four games, you need to find the probability of winning game 1 AND winning game 2 AND winning game 3 AND winning game 4, which is ##P(w1 \cap w2 \cap w3 \cap w4)##. The key word here is "and," as in "the team wins all four games." So, in summary, the probability of the football team winning all four games is 0.75^4, not 1-0.25^4.
  • #1
DODGEVIPER13
672
0

Homework Statement


A football team has a probability of .75 of winning when playing any of the other four teams in its conference. If the games are independent, what is the probability the team wins all the games?


Homework Equations


P(w1 u w2 u w3 u w4)=1-P(w1 u w2 u w3 u w4)' the ' mark stands for complement


The Attempt at a Solution


I found that the complement w=.25, and since it says independent that 1-p(w1)'p(w2)'p(w3)'p(w4)' so 1-.25^4=.996 probability of winning however the book says .75^4 why didn't they do as I did?
 
Physics news on Phys.org
  • #2
Like how do you know when to use .75^4 or what I did in problems what key words will tell me which one?
 
  • #3
You've calculated the probability that the team wins at least one game, not the probability that it wins all four games.

To win at least one game, it has to win game 1 OR game 2 OR game 3 OR game 4.
To win all four games, it has to win game 1 AND game 2 AND game 3 AND game 4.
 
  • #4
Oh ok I get it the complement bar makes the union go to intersection so therefore I calculated the or and not the and.
 
  • #5
It really has nothing to do with taking the complement. You performed your calculation correctly; it just wasn't the right calculation to do. OR corresponds to the union while AND corresponds to the intersection, so ##P(w1 \cup w2 \cup w3 \cup w4)## is the probability of winning game 1 OR winning game 2 OR winning game 3 OR winning game 4.
 

FAQ: Calculating the probability of an event

What is the formula for calculating the probability of an event?

The formula for calculating the probability of an event is: P(E) = Number of favorable outcomes / Total number of possible outcomes.

How do you determine the total number of possible outcomes?

The total number of possible outcomes can be determined by counting all the different ways the event can occur. This may involve using a tree diagram, a table, or combinatorial techniques such as permutations or combinations.

What is the difference between theoretical and experimental probability?

Theoretical probability is the expected probability of an event based on mathematical calculations, while experimental probability is the actual observed probability of an event based on repeated trials or experiments.

Can the probability of an event be greater than 1?

No, the probability of an event cannot be greater than 1. A probability of 1 means that the event is certain to occur, while a probability of 0 means that the event is impossible. Any probability between 0 and 1 represents the likelihood of the event occurring.

How can you use probability to make predictions?

By calculating the probability of an event, you can make predictions about the likelihood of that event occurring. This can help in decision making, risk assessment, and understanding the chances of certain outcomes in various scenarios.

Similar threads

Replies
1
Views
2K
Replies
5
Views
2K
Replies
4
Views
1K
Replies
1
Views
4K
Replies
4
Views
1K
Replies
1
Views
5K
Replies
1
Views
2K
Back
Top