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Hager plays a chess competition - Junior Cycle Mathematics - Question 6 - 2018
Question 6
Hager plays a chess competition. In each game, she can win (W), draw (D), or lose (L). (a) Fill in the table below to show the 9 possible outcomes for Hager's first... show full transcript
Worked Solution & Example Answer:Hager plays a chess competition - Junior Cycle Mathematics - Question 6 - 2018
Step 1
Fill in the table below to show the 9 possible outcomes for Hager's first two games.
Answer
To complete the table for the first two games, we need to consider all combinations of wins (W), draws (D), and losses (L) for both games.
The outcomes for Game 1 are W, D, and L. For Game 2, we also have W, D, and L. Hence, we can fill in the following:
Game 2
W D L
Game 1
W WW WD WL
D DW DD DL
L LW LD LL
Here,:
- WW: Won Game 1 and Game 2
- WD: Won Game 1 and Draw Game 2
- WL: Won Game 1 and Lost Game 2
- DW: Draw Game 1 and Won Game 2
- DD: Draw Game 1 and Draw Game 2
- DL: Draw Game 1 and Lost Game 2
- LW: Lost Game 1 and Won Game 2
- LD: Lost Game 1 and Draw Game 2
- LL: Lost Game 1 and Lost Game 2
Step 2
Work out the total number of different possible outcomes for her 3 games.
Answer
To find the total number of possible outcomes for 3 games, we use the principle of counting. For each game, Hager has 3 possible outcomes: Win (W), Draw (D), or Lose (L).
The total number of outcomes is given by: This means that there are 27 different possible outcomes for Hager playing 3 games.