Subjects probability

Probability Strawberry Chocolate 374C07

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem statement:** Find the probability of drawing a strawberry candy, replacing it, and then drawing a chocolate candy from a jar. 2. **Given:** - Chocolate candies = 6 - Strawberry candies = 10 - Mint candies = 4 - Caramel candies = 5 - Total candies = 6 + 10 + 4 + 5 = 25 3. **Formula for probability:** $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 4. **Step 1: Probability of drawing a strawberry candy:** $$P(\text{strawberry}) = \frac{10}{25}$$ 5. **Step 2: Since the candy is replaced, the total number of candies remains the same. Probability of drawing a chocolate candy next:** $$P(\text{chocolate}) = \frac{6}{25}$$ 6. **Step 3: Probability of both events happening (drawing strawberry then chocolate) with replacement is the product of individual probabilities:** $$P(\text{strawberry then chocolate}) = P(\text{strawberry}) \times P(\text{chocolate}) = \frac{10}{25} \times \frac{6}{25}$$ 7. **Step 4: Simplify the product:** $$\frac{10}{25} \times \frac{6}{25} = \frac{10 \times 6}{25 \times 25} = \frac{60}{625}$$ 8. **Step 5: Simplify the fraction by dividing numerator and denominator by 5:** $$\frac{\cancel{60}^ {12}}{\cancel{625}^{125}} = \frac{12}{125}$$ **Final answer:** $$\boxed{\frac{12}{125}}$$ This means the probability of drawing a strawberry candy, replacing it, and then drawing a chocolate candy is $\frac{12}{125}$.