Probability exactly one event occurs?

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In summary, the conversation is about finding the probability of exactly one event occurring when there is a 0.42 chance of eating cake, a 0.56 chance of eating pie, and a 0.16 chance of eating both. The solution involves creating a Venn diagram and labeling the portions of the circles that are not in the intersection. The correct answer is 0.40 + 0.26 = 0.66.
  • #1
bcahmel
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Probability exactly one event occurs?

Homework Statement



0.42 chance eat cake, 0.56 chance eat pie. 0.16 chance eat both.Find probability that you eat exactly one of these two desserts.

Homework Equations


? I made a venn diagram


The Attempt at a Solution


I know how to find the probability of at least 1, but I don't understand how to find exactly one. At first I thought it would just be 0.40 + 0.26 =0.66 but I don't think this is right? So basically I just added probability eat cake + probability eat pie but I think this results in the probability or eating one or the other. So help? Please?
 
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  • #2


Did you label your Venn diagram? The event "exactly 1" has probability found in the portions of the circles that are not in the intersection.
 
  • #3


Your answer's right. Why do you think it's wrong?
 
  • #4


thanks! I don't know why I think its wrong- stat isn't really common sense for me unfortunately :(
 
  • #5


Just to clarify, your first answer is correct. I think you did something different on your second attempt.
 

FAQ: Probability exactly one event occurs?

What is the definition of probability exactly one event occurs?

Probability exactly one event occurs refers to the likelihood of a specific event happening among multiple possible outcomes. It means that out of all possible outcomes, only one will occur.

How do you calculate the probability of exactly one event occurring?

To calculate the probability of exactly one event occurring, you need to divide the number of desired outcomes by the total number of possible outcomes. The formula is P = n/N, where P is the probability, n is the number of desired outcomes, and N is the total number of possible outcomes.

What is the difference between probability of at least one event and probability of exactly one event occurring?

The probability of at least one event occurring means that out of all possible outcomes, one or more will occur. On the other hand, the probability of exactly one event occurring means that only one specific outcome will occur and no others.

Can the probability of exactly one event occurring be greater than 1?

No, the probability of any event occurring can never 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 will not occur. Any value in between 0 and 1 represents the likelihood of the event occurring.

How does the probability of exactly one event occurring relate to other types of probabilities?

The probability of exactly one event occurring is a specific case of the binomial probability, where there are only two possible outcomes - success or failure. It is also related to the concept of independent events, where the outcome of one event does not affect the likelihood of another event occurring.

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