A bag of candy has 5 red candies, 3 blue candies, and 6 green candies. Let \( X \) be the event of randomly choosing a blue candy. (a) Find \( P(X) \). \( P(X)= \) Enter your answer (b) Find \( P\left(X^{\prime}\right) \). \( P\left(X^{\prime}\right)= \) Enter your answer

To find \( P(X) \), we first need to determine the total number of candies in the bag. We have 5 red, 3 blue, and 6 green candies, which adds up to: \[ 5 + 3 + 6 = 14 \text{ candies} \] Now, the probability of choosing a blue candy, \( P(X) \), is given by the ratio of the number of blue candies to the total number of candies: \[ P(X) = \frac{\text{Number of blue candies}}{\text{Total number of candies}} = \frac{3}{14} \] So, \( P(X) = \frac{3}{14} \). Next, to find \( P(X^{\prime}) \), we need to calculate the probability of not choosing a blue candy. This is represented as \( P(X^{\prime}) \): \[ P(X^{\prime}) = 1 - P(X) = 1 - \frac{3}{14} = \frac{14}{14} - \frac{3}{14} = \frac{11}{14} \] Therefore, \( P(X^{\prime}) = \frac{11}{14} \).