Probability word begins with O, ends with R

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
Mere
Posts: 7
Joined: Fri Aug 07, 2009 3:01 am
Location: USA
Contact:

Probability word begins with O, ends with R

Postby Mere » Sat Aug 08, 2009 12:50 am

Can someone show me how to do this problem? I think that it is conditional probability, but I am unsure how to set up the problem. Thanks...

If the letters in the word "POKER" are rearranged, what is the probability that the word will begin with the letter "O" and end with the letter "R"?

User avatar
stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Sat Aug 08, 2009 1:17 am

In how many ways can you arrange the letters?

If you fix O as the first letter and R as the last, in how many ways can you arrange the other letters?

Divide the latter by the former. :wink:

Mere
Posts: 7
Joined: Fri Aug 07, 2009 3:01 am
Location: USA
Contact:

Re: Probability word begins with O, ends with R

Postby Mere » Sat Aug 08, 2009 1:29 am

So...

If you can arrange all of the letters in "POKER" in 120 ways, and
you can arrange letters "PKE" (with O and R on the outside) in 6 ways,
would it be 6/120?

User avatar
stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Sat Aug 08, 2009 2:01 am

Mere wrote:...would it be 6/120?

Your reasoning looks good to me! :D

Just remember to simplify your answer before you hand it in. :wink:


Return to “Discrete Math”