Question

You are to play three games. In the first game, you draw a card, and you win if the card is a heart. In the second game, you toss two coins, and you win if one head and one tail are shown. In the third game, two dice are rolled and you win if the sum of the dice is 7 or 11. What is the probability that you win all three games? What is the probability that you win exactly two games?

Solve the question using Tree Diagram. Please give explanation for the answer.

Answer 1

Probabilities of winning in each game

Game 1:

= Number of heart cards / Total number of cards in a deck = 13/52 = 0.25

Game 2:

= Probability of getting HT or TH in tossing two coins = 1/2 = 0.5

Game 3:

= Probability of getting the events {16, 25, 34, 43, 52, 56, 61, 65} in tossing two coins

= 8/36

= 0.2222

Hence, Probabilities of losing in each game are:

Now consider the Tree Diagram:

From the above tree diagram,

Probability of winning all Three Games = Probability of WWW = 0.0278

Probability of winning exactlly two games = Probability of WWL + Probability of WLW + Probability of LWW

= 0.0972 + 0.0278 + 0.0833

= 0.2083

Hence, the probability that you win all three games is 0.0278.

And, the probability that you win exactly two games is 0.2083.