How Do You Calculate Probabilities for Multiple Coin Tosses?

[gtpdriver]

Im just starting probability and need some help. I have a question in my text that i can't figure out.

Three coins are tossed at the same time. Find the probability that
a) all come up heads
b) at least one comes up tails
c) exactly two come up heads


I know that the total possible outcomes is 8 but i don't know how to figure out the outcomes of the event.


Thanks for any help!

Adam

 

[shmoe]

Hi, since there are only 8 possible outcomes, why don't you start by writing down all of them and see how often each event occurs? Once you've done that, see if you can come up with a more clever approach that will work for more general circumstances.

 

[dextercioby]

For the first part,i'm sure you realize that there are independent events involved...
What is the number of favorable outcomes for points b) and c)...?

Daniel.

P.S.The problem is so simple,you can even count them...But that's only for checking your logics...It could have been 100 coins being flipped at the same time...

 

[gtpdriver]

Yeah I figured it out after i posted the question...oh well.

Thanks anyways

 

[The Divine Zephyr]

Remember, if multiple events need to cooexist, multiply their probabilities together (similar to an "AND" gate in programming) and if either goes, add their probabilites (similar to "OR" gates)

 

[Alkatran]

Remember, if multiple events need to cooexist, multiply their probabilities together (similar to an "AND" gate in programming) and if either goes, add their probabilites (similar to "OR" gates)

No no no. If either goes, add their probabilties and subtract the AND. Otherwise you count the center twice.

A and B = A + B - (A or B)
Check out a Venn diagram for a better idea of what's going on.