Non-mutually exclusive probability? Help!

bjn201

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Feb 10, 2017
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Hi

My 16 year old son had a question in one of his exams about probability that I could not answer - could anyone help?

I know that P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y)


However the problem was this:

Probability of number of goals in a football/soccer game:

probability of more than one goal: 90% (9/10)
probability of less than 4 goals: 85% (8/10)

No further information was given

What is the probability of more than one goal but less than 4 goals?

Am i using the right formula? are these non-mutually exclusive?

Thanks!
 
No, that formula isn't quite what you need. Try replacing the symbols with the words they represent and you'll see why:

P(X OR Y) = P(X) + P(Y) - P(X AND Y)

Let P(X) be the probability of scoring more than one goal, and P(Y) be the probability of scoring less than four goals. Now, the problem text asks you to find "the probability of [scoring] more than one goal but less than 4 goals?" From this, we know that we need both events, X, AND Y to occur. You ask if the events X and Y are mutually exclusive. Well, the definition of "mutually exclusive" is that the events cannot happen at the same time. So, can these two events both happen?

The final thing you'll need to find out is if the events are independent. The definition of "Independent Events" is that the probability of X happening doesn't affect the probability of Y happening. So, if the team scores more than one goal, does that change the probability of them scoring less than four goals? Now, how can you put all of this information together to solve the problem?

If you (or your son) need a refresher on some of these subjects, the page I linked for independent events has some information and formulas you might find useful in solving this problem. :)
 
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