Question

7 clinton has a bag of skittles™. inside the bag are 6 red, 4 orange, 7 yellow, 3 purple and 4 green skittles™. what is the probability of drawing a green skittle™, replacing it, and then drawing another green skittle™?

Explanation:

Step1: Calculate total number of Skittles

First, we find the total number of Skittles by adding the number of each color. The number of red is 6, orange is 4, yellow is 7, purple is 3, and green is 4. So total \( n = 6 + 4 + 7 + 3 + 4 \)
\( n = 24 \)

Step2: Probability of drawing a green Skittle

The number of green Skittles is 4. The probability of drawing a green Skittle, \( P(\text{green})=\frac{\text{number of green}}{\text{total number}}=\frac{4}{24}=\frac{1}{6} \)

Step3: Probability of two independent events (with replacement)

Since we replace the Skittle, the two events (drawing green first and then green again) are independent. The probability of two independent events \( A \) and \( B \) is \( P(A \cap B)=P(A)\times P(B) \). Here, both events are drawing a green Skittle, so \( P(\text{green then green}) = P(\text{green}) \times P(\text{green}) \)
Substituting the value of \( P(\text{green})=\frac{1}{6} \), we get \( \frac{1}{6} \times \frac{1}{6}=\frac{1}{36} \)

Answer:

\(\frac{1}{36}\)