Probabillity of an event happening given union and intersection

[thisischris]

Hello everyone.. I'm stuck on this and don't really know what equations to apply or how you get the answer.

An and Kat go on each Friday to the cinema independently of each other. On any given Friday the probability of both going to the cinema is 1/3. And the probability that at least one of them goes is 5/6.

Find the possible values for the probability that An goes to the cinema on a Friday.

The answer at the back is 1/2 or 2/3.

Thank you!

 

[Ray Vickson]

Hello everyone.. I'm stuck on this and don't really know what equations to apply or how you get the answer.

An and Kat go on each Friday to the cinema independently of each other. On any given Friday the probability of both going to the cinema is 1/3. And the probability that at least one of them goes is 5/6.

Find the possible values for the probability that An goes to the cinema on a Friday.

The answer at the back is 1/2 or 2/3.

Thank you!

Use the principle of inclusion/exclusion to get P{at least one goes} in terms of P{An goes}, P{Kat goes} and P{both go}.

RGV

 

[thisischris]

Use the principle of inclusion/exclusion to get P{at least one goes} in terms of P{An goes}, P{Kat goes} and P{both go}.

RGV

It does not seem like the syllabus covers this. Strange. Could you point me to any reference/tutorial that explains it possibly?

Thank you.

 

[Ray Vickson]

It does not seem like the syllabus covers this. Strange. Could you point me to any reference/tutorial that explains it possibly?

Thank you.

So, it appears nowhere in your textbook? That is very strange, since it is so basic it is covered in every introductory probability course. However, if what you say is true, you can use Google to find everything you need; just search for "inclusion-exclusion principle"---but don't worry if the first article is too hard to follow---just look farther down the list. Just drawing a Venn diagram should give you everything you need, and some of the tutorials you get through Google lay it out in detail.

RGV

 

[jing2178]

As an alternative if you have covered tree diagrams you could use one to find the results. See the attached diagram and use it to form equations which you can solve for p.