1. **State the problem:** We have an abbreviated deck with 20 cards: 4 Jacks, 4 Queens, 4 Kings, 4 Aces, and 4 10s. Each type has one card of each suit (hearts, diamonds, spades, clubs). We want to check if the events "Picking a Jack" and "Picking a diamond" are independent. 2. **Recall the definition of independence:** Two events $A$ and $B$ are independent if and only if $$P(A \cap B) = P(A) \times P(B).$$ 3. **Calculate $P(\text{Jack})$:** There are 4 Jacks out of 20 cards, so $$P(\text{Jack}) = \frac{4}{20} = \frac{1}{5}.$$ 4. **Calculate $P(\text{Diamond})$:** There are 5 types of cards, each with one diamond, so total diamonds = 5. Thus, $$P(\text{Diamond}) = \frac{5}{20} = \frac{1}{4}.$$ 5. **Calculate $P(\text{Jack} \cap \text{Diamond})$:** There is exactly one Jack of diamonds, so $$P(\text{Jack} \cap \text{Diamond}) = \frac{1}{20}.$$ 6. **Check independence:** Calculate $$P(\text{Jack}) \times P(\text{Diamond}) = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20}.$$ Since $$P(\text{Jack} \cap \text{Diamond}) = P(\text{Jack}) \times P(\text{Diamond}),$$ the events are independent. **Final answer:** The statement "Picking a Jack and picking a diamond are independent events" is **true**.