Question

juan and neo play a game. each player holds out a hand at the same moment to represent a rock, paper, or scissors. then they each choose one of the three items. create a list, table, or tree diagram to represent all the possible combinations of choices. what is the probability that they both choose the same object?

Explanation:

Step1: List all possible combinations

Let R represent rock, P represent paper, and S represent scissors. The possible combinations of Juan's and Neo's choices are: (R,R), (R,P), (R,S), (P,R), (P,P), (P,S), (S,R), (S,P), (S,S).

Step2: Calculate total number of combinations

There are 3 choices for Juan and 3 choices for Neo. By the multiplication principle, the total number of combinations is $3\times3 = 9$.

Step3: Count favorable combinations

The favorable combinations (where they choose the same object) are (R,R), (P,P), (S,S), so there are 3 favorable combinations.

Step4: Calculate probability

The probability $P$ that they both choose the same object is the number of favorable combinations divided by the total number of combinations. So $P=\frac{3}{9}=\frac{1}{3}$.

Answer:

The list of all possible combinations is: (R,R), (R,P), (R,S), (P,R), (P,P), (P,S), (S,R), (S,P), (S,S). The probability that they both choose the same object is $\frac{1}{3}$.