Math  /  Data & Statistics

QuestionPart A: Ontario's Alpine Skiers An alpine ski coach in Ontario wants insight on how alpine skiers from the province are performing in the Slalom, Giant Slalom, and Super G events in national competitions. A random sample of 74 Ontario alpine skiers who completed in the Canada Winter Games between 1983 and 2015 is selected. The following table summarizes the places in which alpine skiers finish in each of the three events. This table can be found in the Excel sheet Ontario and Quebec. \begin{tabular}{|c|c|c|c|} \hline & Place \#1 to.\#3 (Medals) & Place \#4 to \#10 & Remaining Places \\ \hline Slalom & 3 & 10 & 11 \\ \hline Giant Slalom & 5 & 9 & 16 \\ \hline Super G & 4 & 8 & 8 \\ \hline \end{tabular} (i) If an Chtarian alpine skier is chosen at random, what is the probability that they received a medal in their event?

Studdy Solution

STEP 1

1. The total number of alpine skiers sampled is 74.
2. Medals are awarded to skiers who finish in places #1 to #3.
3. The probability is calculated as the number of medal-winning skiers divided by the total number of skiers.

STEP 2

1. Calculate the total number of medal-winning skiers.
2. Calculate the probability of a skier winning a medal.

STEP 3

Identify the number of medal-winning skiers in each event:
- Slalom: 3 skiers - Giant Slalom: 5 skiers - Super G: 4 skiers

STEP 4

Calculate the total number of medal-winning skiers:
3+5+4=12 3 + 5 + 4 = 12

STEP 5

Calculate the probability of a skier winning a medal:
Probability=Total medal-winning skiersTotal skiers=1274 \text{Probability} = \frac{\text{Total medal-winning skiers}}{\text{Total skiers}} = \frac{12}{74}

STEP 6

Simplify the probability fraction:
1274=637 \frac{12}{74} = \frac{6}{37}
The probability that a randomly chosen Ontario alpine skier received a medal is:
637 \boxed{\frac{6}{37}}

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