Junior Cycle Mathematics Counting/Permutations: When Maeve's team play a match,

When Maeve's team play a match, they can win (W), draw (D), or lose (L) - Junior Cycle Mathematics - Question 2 - 2022

Question 2

When Maeve's team play a match, they can win (W), draw (D), or lose (L). When Maeve's team play two matches, one is already done. W D means they win Match 1 and dra... show full transcript

Worked Solution & Example Answer:When Maeve's team play a match, they can win (W), draw (D), or lose (L) - Junior Cycle Mathematics - Question 2 - 2022

Step 1

Fill in the table below to show the 9 possible outcomes when Maeve's team play two matches.

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Answer

To complete the table, we consider the outcomes from both matches. The completed table is as follows:

Match 1	Match 2
W	W
W	D
W	L
D	W
D	D
D	L
L	W
L	D
L	L

Step 2

Maeve thinks that each outcome in the table is equally likely. Based on this, find the probability that, when Maeve's team play two matches, they win at least one match. Give your answer as a fraction.

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Answer

To find the probability of winning at least one match, we first note that there are a total of 9 outcomes (as shown in the table). The outcomes where Maeve's team wins at least one match are:

This gives us a total of 5 favorable outcomes. Thus, the probability is calculated as:

$P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{9}$

Step 3

Maeve's team play 5 matches in a competition. Work out the total number of different possible outcomes for Maeve's team for these 5 matches.

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Answer

For each match, there are 3 possible outcomes: Win (W), Draw (D), or Lose (L). Therefore, for 5 matches, the total number of different possible outcomes can be calculated using the formula:

$Total \ outcomes = 3^5$

Calculating this gives:

$3^5 = 243$

Thus, Maeve's team has a total of 243 different possible outcomes for the 5 matches.

When Maeve's team play a match, they can win (W), draw (D), or lose (L) - Junior Cycle Mathematics - Question 2 - 2022

Worked Solution & Example Answer:When Maeve's team play a match, they can win (W), draw (D), or lose (L) - Junior Cycle Mathematics - Question 2 - 2022

Fill in the table below to show the 9 possible outcomes when Maeve's team play two matches.

Maeve thinks that each outcome in the table is equally likely. Based on this, find the probability that, when Maeve's team play two matches, they win at least one match. Give your answer as a fraction.

Maeve's team play 5 matches in a competition. Work out the total number of different possible outcomes for Maeve's team for these 5 matches.

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