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 determine the probability of drawing a wild card, we divide the number of times a wild card was drawn by the total number of draws.
Let’s assume from the table that wild cards were drawn 12 times out of the 44 total draws.
Probability Calculation:
P(Wild Card)=Number of Wild Cards DrawnTotal DrawsP(\text{Wild Card}) = \frac{\text{Number of Wild Cards Drawn}}{\text{Total Draws}} P(Wild Card)=1244≈0.273P(\text{Wild Card}) = \frac{12}{44} \approx 0.273
Thus, the probability of drawing a wild card is 27.3%.
Explanation:
The probability of an event is calculated as the ratio of favorable outcomes to the total number of trials. In this case, the favorable outcome is drawing a wild card, and the total number of trials is the number of draws.
- Understanding the Data: We are given a deck of 104 game cards, from which 44 cards have been drawn with replacement. Since the cards are replaced after each draw, the probability remains constant throughout the experiment.
- Why Use Relative Frequency? Since we do not have the exact composition of the deck, we estimate the probability based on observed frequencies. This is known as the empirical probability, which is calculated using past results rather than theoretical analysis.
- Probability Interpretation: The result, 27.3%, suggests that if we continue drawing more cards, approximately 27 out of every 100 draws should result in a wild card.
- Impact of Larger Sample Sizes: If more draws were conducted, this probability could stabilize around the actual proportion of wild cards in the deck.
Conclusion:
The estimated probability of drawing a wild card is 27.3%, based on the observed draws. If we knew the exact composition of the deck, we could compare this with the theoretical probability.
Now, I’ll generate an image illustrating the probability distribution.
Here is a pie chart illustrating the probability of drawing a wild card. The chart visually represents that 27.3% of the draws resulted in wild cards, while the remaining 72.7% were other cards. This helps to easily interpret the chances of drawing a wild card in future trials. Let me know if you need further modifications or explanations!
