Probability problem question

[NoMoreExams]

I would find an expression for each series and see where they are equal... isn't that what you are trying to accomplish?

[ronaldy27]

How would you answer this question? Would you list all the numbers that are equal? Is there a short cut?

[NoMoreExams]

A number X is chosen at random from the series 2,5,8,... and another number Y is chosen at random from the series 3,7,11,.. Each series has 100 terms. Find P[X=Y].

This isn't a hard question but I forgot how to manipulate series from calculus.
How would you approach this problem? I can do this problem by listing all the numbers that matches but how can you do this without listing?

Are you trying to figure out the general term in each series? For example the first one would be 3n + 2 for n = 0, 1....

[ronaldy27]

A number X is chosen at random from the series 2,5,8,... and another number Y is chosen at random from the series 3,7,11,.. Each series has 100 terms. Find P[X=Y].

This isn't a hard question but I forgot how to manipulate series from calculus.
How would you approach this problem? I can do this problem by listing all the numbers that matches but how can you do this without listing?