### Jewelry Classification and Probability Exercise **Overview:** 550 pieces of jewelry are categorized based on two attributes: 1. Type: Necklace, Bracelet, Earrings. 2. Color: White Gold (W), Rose Gold (R), Yellow Gold (Y). **Jewelry Classification Table:** | Type of Jewelry | White (W) | Rose (R) | Yellow (Y) | Total | |-----------------|-----------|----------|------------|-------| | Necklace (N) | 80 | 70 | 60 | 210 | | Bracelet (B) | 20 | 40 | 55 | 115 | | Earrings (E) | 30 | 95 | 100 | 225 | | **Total** | **130** | **205** | **215** | **550** | **Probability Questions:** Given that one item is selected at random, calculate the following probabilities: (a) \( P(W) \): Probability of selecting a white gold piece. (b) \( P(B) \): Probability of selecting a bracelet. (c) \( P(W \cap E) \): Probability of selecting white gold earrings. (d) \( P(B / R) \): Probability of selecting a bracelet given that it's rose gold. (e) \( P(R \cup E) \): Probability of selecting either a rose gold item or a pair of earrings. (f) \( P(Y / E) \): Probability of selecting a yellow gold item given that it's earrings. (g) \( P(N') \): Probability of selecting an item that is not a necklace. (h) \( P(W \cup R / E') \): Probability of selecting either a white or rose gold item given that it's not earrings.