2. A dice is rolled. A card is drawn from a deck of face cards (i. e. only Jack, Queen, King of each suit). A coin is flipped. a) Draw a tree diagram to define the sample space for this game. b) You win the game if you toss tails, draw a heart, and roll an even number. Find the probability that you do not win.

When you roll and even number, the probability of winning is 3/6 or 1/2.

When you want to draw a heart:

The sample space is 12. That is 3 faces and 4 suits. There are 4 hearts in this deck. The probability you get a heart is 4/12 or 1/3.

When you want to toss a tail:

Sample space is 2, hea d and tail. You do not win if you get a heads. The probability is 1/2. The probability of winning is 1/2 * 1/3 * 1/2 = 1/12 Then the probability of losing is 1-1/12 = 11/12