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 (call this event H), 15% of students purchased a new pair of sunglasses (call this event G) and 6% of students purchased both a pair of short and a pair of sunglasses. [br][br]9. Find the probability that a student purchased a pair of sunglasses given that you know they purchased a pair of shorts. P (G|H) = [br][br]10. Find the probability that a student purchased a pair of shorts or purchased a new pair of sunglasses. [br]P (H ∪ G) = [br][br]11. Given the condition that you know a student has purchased at least one of the items. What is the probability that they purchased only one of the items? [br][br][br]12. Are the two events H and G independent of one another? Why or Why not?

Answer parts a-f below.