The table shows the results of drawing 44 cards from a deck of 104 game cards. After each draw, the card is replaced. Based on the results, what is the chance that a draw results in a wild card?
The Correct Answer and Explanation is:
To find the chance that a draw results in a wild card, we analyze the data provided in the table:
- Total draws: 44
- Wild card draws: 10
Step-by-Step Calculation:
The probability PPP of drawing a wild card is calculated using:P(wild card)=Number of wild card drawsTotal number of draws=1044P(\text{wild card}) = \frac{\text{Number of wild card draws}}{\text{Total number of draws}} = \frac{10}{44}P(wild card)=Total number of drawsNumber of wild card draws=4410
Simplify the fraction:1044=522\frac{10}{44} = \frac{5}{22}4410=225
✅ Correct Answer: 5/22
📘 Explanation
In this problem, you are given the results of an experiment in which cards were drawn 44 times from a deck of 104 cards, with the card replaced after each draw. Replacement ensures that the probability remains constant across all draws, allowing us to use the observed frequencies as a reliable basis for estimating probability.
There are three types of cards in the table: wild cards, number cards, and penalty cards. The frequencies of each type after 44 draws are:
- Wild Cards: 10 times
- Number Cards: 32 times
- Penalty Cards: 2 times
To determine the probability of drawing a wild card, divide the number of wild card draws by the total number of draws. This is a simple relative frequency calculation. The formula used is:Probability=Frequency of EventTotal Trials\text{Probability} = \frac{\text{Frequency of Event}}{\text{Total Trials}}Probability=Total TrialsFrequency of Event
Here, the event is drawing a wild card, and the total number of trials is the number of total draws (44). Substituting the values:1044=522\frac{10}{44} = \frac{5}{22}4410=225
This fraction is already in its simplest form, so the final answer is 5/22.
Even though the original deck has 104 cards, the question is based solely on the results of the experiment (the 44 draws), so the 104 is not directly needed in this probability calculation.
This approach helps students develop an understanding of empirical probability, which is based on actual experiments or observations, unlike theoretical probability which is based on known possible outcomes.
