Score: 0 of 2 points Data gathered on the shopping patterns during the months of April and May of high school students from Peanut Village revealed the following. \( 38 \% \) of students purchased a new pair of shorts (event H ), \( 15 \% \) of students purchased a new pair of sunglasses (event G), and \( 6 \% \) of students purchased both a pair of shorts and a pair of sunglasses. Find the probability that a student purchased a pair of shorts given or purchased a new pair of sunglasses \( P(H \cup G)= \) Enter your answer

To calculate the probability that a student purchased either a new pair of shorts or a new pair of sunglasses, we can use the formula for the union of two events: \[ P(H \cup G) = P(H) + P(G) - P(H \cap G) \] Where: - \( P(H) = 0.38 \) (the probability of purchasing shorts) - \( P(G) = 0.15 \) (the probability of purchasing sunglasses) - \( P(H \cap G) = 0.06 \) (the probability of purchasing both) Now, plug the values into the formula: \[ P(H \cup G) = 0.38 + 0.15 - 0.06 \] \[ P(H \cup G) = 0.38 + 0.15 - 0.06 = 0.47 \] So, the probability that a student purchased a pair of shorts or a new pair of sunglasses is \( P(H \cup G) = 0.47 \).