Jim and Renee will play one game of...

[RonPurewal]

Shouldnt it be this?

Jim picks Rock, AND Renee picks Scissors. (1/3 * 1) = 1/3
Jim picks Scissors, AND Renee picks Paper. (1/3 * 1) = 1/3
Jim picks Paper, AND Renee picks Rock. (1/3 * 1) = 1/3

well, you should know right away that this is incorrect, because it gives an absurd answer.
if you add these up, you arrive at a probability of 1 that jim will win. it is clearly not certain that jim will win, so a probability of 1 is incorrect.

Reason for "1". If Jim picks rock, Renee has only 1 option in order to make Jim win, which is to pick Scissor and hence probability of 1 for Renee.

...right, but that's not how probabilities work.
this is the right reasoning for finding the numerator of a probability expression. however, the denominator still has to be the total number of possibilities (in this case, 3 for each situation considered).

--

you can also consider the entire problem at once, as follows:
* renée has to pick something
* once renée has picked something, jim will always have 3 options, exactly 1 of which will win.
* therefore, the desired probability is 1/3.

[gps470]

Pretty old thread, but I couldn't resist posting. I faced this question in the mock test today. I think the question stem should convey this clearly, that both Jim and Renee have their own copies of the 3 signs. If that is not the case, which is what I assumed, answer would be 1/2, since there cannot be any ties, and both are equally probable to win/lose regardless of who picks first/last.
Alternatively, the question can say "select with replacement".

[tim]

"both Jim and Renee have an equal chance of choosing any one of the hand signs"

This quote from the problem itself does exactly what you're asking. If that wasn't clear to you, it is not an issue with the problem, but with your interpretation. You'll want to make sure you recognize that this question says exactly what it is supposed to.

[gps470]

"both Jim and Renee have an equal chance of choosing any one of the hand signs"

This quote from the problem itself does exactly what you're asking. If that wasn't clear to you, it is not an issue with the problem, but with your interpretation. You'll want to make sure you recognize that this question says exactly what it is supposed to.

Good catch Tim. I just looked at "each will select and show a hand sign for one of the three items" and glanced through "assuming that both Jim and Renee have an equal chance....". Another reason to pay close attention.

Thanks

[RonPurewal]

yep. read slowly.

if you read slowly, you'll actually get through the exam faster!