Answer :
Certainly! Let's explain why Whitney's statement about the probability of picking a green counter is correct.
### Step-by-Step Explanation:
1. Identify the Total Number of Counters:
- There are 3 green counters in the bag.
- Let [tex]\( n \)[/tex] represent the number of yellow counters in the bag.
- Therefore, the total number of counters in the bag is the sum of the green and yellow counters, which is [tex]\( 3 + n \)[/tex].
2. Understand the Probability Formula:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this context, picking a green counter is the favorable outcome.
3. Determine the Number of Favorable Outcomes:
- The number of green counters is the number of favorable outcomes.
- There are 3 green counters.
4. Calculate the Probability:
- The total number of possible outcomes is the total number of counters, which is [tex]\( 3 + n \)[/tex].
- Therefore, the probability [tex]\( P \)[/tex] of picking a green counter is given by:
[tex]\[ P(\text{green}) = \frac{\text{number of green counters}}{\text{total number of counters}} = \frac{3}{3 + n} \][/tex]
### Conclusion:
Whitney is correct because the probability of picking a green counter is the number of green counters (which is 3) divided by the total number of counters (which is [tex]\( 3 + n \)[/tex]). This is represented by the fraction [tex]\( \frac{3}{3+n} \)[/tex].
Thus, Whitney's statement accurately reflects the calculation of the probability of picking a green counter in this scenario.
### Step-by-Step Explanation:
1. Identify the Total Number of Counters:
- There are 3 green counters in the bag.
- Let [tex]\( n \)[/tex] represent the number of yellow counters in the bag.
- Therefore, the total number of counters in the bag is the sum of the green and yellow counters, which is [tex]\( 3 + n \)[/tex].
2. Understand the Probability Formula:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this context, picking a green counter is the favorable outcome.
3. Determine the Number of Favorable Outcomes:
- The number of green counters is the number of favorable outcomes.
- There are 3 green counters.
4. Calculate the Probability:
- The total number of possible outcomes is the total number of counters, which is [tex]\( 3 + n \)[/tex].
- Therefore, the probability [tex]\( P \)[/tex] of picking a green counter is given by:
[tex]\[ P(\text{green}) = \frac{\text{number of green counters}}{\text{total number of counters}} = \frac{3}{3 + n} \][/tex]
### Conclusion:
Whitney is correct because the probability of picking a green counter is the number of green counters (which is 3) divided by the total number of counters (which is [tex]\( 3 + n \)[/tex]). This is represented by the fraction [tex]\( \frac{3}{3+n} \)[/tex].
Thus, Whitney's statement accurately reflects the calculation of the probability of picking a green counter in this scenario.
