The problem shown in the image involves a two-way frequency table with information about the scores of contestants from the United States and Canada in a crossword puzzle competition. The table is as follows:

• United States:

  • Up to 100 points: 2
  • Over 100 points: 4

• Canada:

  • Up to 100 points: 4
  • Over 100 points: 2

The question asks: "What is the probability that a randomly selected contestant scored over 100 points given that the contestant is from Canada?"

To solve this, we use conditional probability. The formula for conditional probability is:

$P(\text{Over 100 points | Canada}) = \frac{P(\text{Over 100 points and Canada})}{P(\text{Canada})}$

1. P(Over 100 points and Canada) is the number of Canadian contestants who scored over 100 points. From the table, this number is 2.

2. P(Canada) is the total number of Canadian contestants. From the table, the total for Canada is $4 + 2 = 6$.

Now, apply the formula:

$P(\text{Over 100 points | Canada}) = \frac{2}{6} = \frac{1}{3}$

So, the probability is $\frac{1}{3}$, or approximately 0.3333.

Let me know if you'd like further clarification or have more questions!

Related Questions:

1. What is the probability that a randomly selected contestant scored under 100 points given they are from the United States?
2. How do you calculate the overall probability that a contestant scored over 100 points across both countries?
3. If there were 10 more Canadian contestants, how would this change the probability for a Canadian scoring over 100 points?
4. How does the concept of conditional probability apply in real-world scenarios such as medical testing or marketing?
5. Can you explain the difference between independent and dependent events using the given table?

Tip:

For conditional probability, always remember to use the ratio of the number of favorable outcomes for the event of interest to the total number of possible outcomes in the given condition.