In: Statistics and Probability
A game show has a host and three contestants. Suppose the three contestants are Meg, Tyler and Ashley. The host and each contestant each have a bag with 3 marbles; one red, one white and one blue. The host will choose a marble from her bag, then Meg will choose a marble from her bag. If Meg’s marble is the same color as the host, then Meg has won and the game is over. If Meg loses, then Tyler will choose a marble from his bag. If Tyler chooses a marble the same color as the host or Meg, then he wins. If Tyler does not win then Ashley will choose a marble from her bag. Well, from here you can probably guess what it takes for Ashley to either win or lose. (Each choice will be random.)
A: Does every contestant have a chance to win? Explain.
B: Is it possible for none of the contestants to win? Explain.
C: Why are these first two questions important to ask and answer?
D: Is one contestant more likely to win than the other two? Explain.
E: Calculate the probability of a win for each contestant.