karen and jake are playing rock-paper-scissors. make a tree diagram to show the outcomes and winners for each round.

a. what is the probability that karen chooses paper? Show your work.

b. what is the probability that karen chooses rock and jake chooses paper? Show your work.

c. what is the probability that karen wins the game?Show your work.

d. what is the probability that jake wins the game?Show your work.

e. what is the probability the game will end in a tie?Show your work.

f. If karen and jake play the game 60 times, what is the predicted number of times that karen will win? Show your work.