Question

1. karen has a fun-size bag of skittles™. inside the bag are 2 red, 4 orange, 2 yellow, 2 purple and 2 green skittles™. what is the probability of drawing an orange skittle™, eating it, and then drawing a purple skittle™?

Explanation:

Step1: Calculate total number of Skittles

First, we find the total number of Skittles initially. The number of red is 2, orange is 4, yellow is 2, purple is 2, and green is 2. So total \( n = 2 + 4 + 2 + 2 + 2 = 12 \).

Step2: Probability of drawing orange first

The probability of drawing an orange Skittle first is the number of orange Skittles divided by total Skittles. So \( P(\text{orange})=\frac{4}{12}=\frac{1}{3} \).

Step3: Total Skittles after eating orange

After eating one orange Skittle, the total number of Skittles becomes \( 12 - 1 = 11 \).

Step4: Probability of drawing purple next

The number of purple Skittles is still 2. So the probability of drawing a purple Skittle now is \( P(\text{purple after orange})=\frac{2}{11} \).

Step5: Probability of both events

Since these are dependent events, we multiply the probabilities. So \( P = \frac{1}{3}\times\frac{2}{11}=\frac{2}{33} \).

Answer:

\(\frac{2}{33}\)