Answer :
Let's break down how to find the probability that Lin gets another turn by understanding the components involved:
### Step-by-Step Solution:
1. Determine the possible outcomes for the number cube:
- A standard number cube (die) has 6 faces, each numbered from 1 to 6.
- Therefore, the total number of outcomes for the number cube is 6.
2. Determine the possible outcomes for the deck of cards:
- The deck consists of 10 cards, each uniquely numbered from 1 to 10.
- Therefore, the total number of outcomes for the deck of cards is 10.
3. Identify the favorable outcomes where Lin gets another turn:
- Lin gets another turn if the number on the die matches the number on the drawn card.
- Since the die shows numbers from 1 to 6, we can only consider the cases where the number on the card also falls within this range (1 to 6).
- For each number face on the die (1, 2, 3, 4, 5, and 6), there must be a matching card in the deck.
- Therefore, there are 6 favorable outcomes.
4. Calculate the total number of possible outcomes:
- Each roll of the die can correspond to any of the 10 cards (any combination of outcomes).
- Thus, the total number of possible outcomes is [tex]\( 6 \times 10 = 60 \)[/tex].
5. Calculate the probability of the favorable outcomes:
- There are 6 favorable outcomes where the number on the die matches the number on the drawn card.
- The probability [tex]\( P \)[/tex] is given by the ratio of favorable outcomes to total possible outcomes:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{6}{60} = \frac{1}{10} \][/tex]
6. Represent the probability in the required format:
- As a fraction: [tex]\( \frac{1}{10} \)[/tex]
- As a decimal: 0.1
- As a percentage: 10%
### Conclusion:
The probability that Lin gets another turn is [tex]\( \frac{1}{10} \)[/tex], or 0.1 in decimal form, which is equivalent to 10%.
### Step-by-Step Solution:
1. Determine the possible outcomes for the number cube:
- A standard number cube (die) has 6 faces, each numbered from 1 to 6.
- Therefore, the total number of outcomes for the number cube is 6.
2. Determine the possible outcomes for the deck of cards:
- The deck consists of 10 cards, each uniquely numbered from 1 to 10.
- Therefore, the total number of outcomes for the deck of cards is 10.
3. Identify the favorable outcomes where Lin gets another turn:
- Lin gets another turn if the number on the die matches the number on the drawn card.
- Since the die shows numbers from 1 to 6, we can only consider the cases where the number on the card also falls within this range (1 to 6).
- For each number face on the die (1, 2, 3, 4, 5, and 6), there must be a matching card in the deck.
- Therefore, there are 6 favorable outcomes.
4. Calculate the total number of possible outcomes:
- Each roll of the die can correspond to any of the 10 cards (any combination of outcomes).
- Thus, the total number of possible outcomes is [tex]\( 6 \times 10 = 60 \)[/tex].
5. Calculate the probability of the favorable outcomes:
- There are 6 favorable outcomes where the number on the die matches the number on the drawn card.
- The probability [tex]\( P \)[/tex] is given by the ratio of favorable outcomes to total possible outcomes:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{6}{60} = \frac{1}{10} \][/tex]
6. Represent the probability in the required format:
- As a fraction: [tex]\( \frac{1}{10} \)[/tex]
- As a decimal: 0.1
- As a percentage: 10%
### Conclusion:
The probability that Lin gets another turn is [tex]\( \frac{1}{10} \)[/tex], or 0.1 in decimal form, which is equivalent to 10%.
