Answer to Question #289725 in Statistics and Probability for Nick

Question

A jar contains 8 green, 4 blue, 10 red and 2 yellow skittles A skittle is randomly drawn Replaced then another is drawn Find each probability blue

Answer 1

There are $8+4+10+2=24$ skittles.

When you sample with replacement, your two items are independent. In other words, one does not affect the outcome of the other. You have 4 out of 24 chance of getting the blue skittle in the first drawing and 4 out of 24 chance of getting the blue skittle in the second drawing. We simply find the product of the probabilities of the event directly

$$P(Blue\ Blue)=P(Blue)P(Blue)$$

$$=\dfrac{4}{24}(\dfrac{4}{24})=\dfrac{1}{36}$$