14. A card is drawn from a deck of 52 cards and a die is tossed. What is the probability of: a. Drawing a heart and tossing a 1 ? b. Drawing a heart or tossing a 1 ? c. Drawing a face card and tossing an even number? d. Drawing a face card or tossing an even number?

We have two independent actions: drawing a card from a standard deck of 52 cards and tossing a die. We'll denote the following events: • H: drawing a heart • F: drawing a face card (Jack, Queen, or King) • T₁: tossing a 1 • E: tossing an even number (2, 4, or 6) Now, let’s solve each part step by step. ────────────────────────────── a. Drawing a heart and tossing a 1 • Probability of drawing a heart, P(H) = 13/52 = 1/4 • Probability of tossing a 1, P(T₁) = 1/6 Since the two events are independent, the probability is:   P(H and T₁) = P(H) × P(T₁) = (1/4) × (1/6) = 1/24 ────────────────────────────── b. Drawing a heart or tossing a 1 For the union of two events (H or T₁), we use the formula:   P(H or T₁) = P(H) + P(T₁) − P(H and T₁) Substitute the known values:   P(H or T₁) = 1/4 + 1/6 − 1/24 Convert to a common denominator (24):   1/4 = 6/24, 1/6 = 4/24, and P(H and T₁) = 1/24 Thus:   P(H or T₁) = 6/24 + 4/24 − 1/24 = (6 + 4 − 1)/24 = 9/24 = 3/8 ────────────────────────────── c. Drawing a face card and tossing an even number • There are 12 face cards in a 52-card deck, so P(F) = 12/52 = 3/13 • There are 3 even numbers on a die (2, 4, 6), so P(E) = 3/6 = 1/2 Since these are independent events, we have:   P(F and E) = P(F) × P(E) = (3/13) × (1/2) = 3/26 ────────────────────────────── d. Drawing a face card or tossing an even number Using the union formula:   P(F or E) = P(F) + P(E) − P(F and E) Substitute the probabilities:   P(F or E) = 3/13 + 1/2 − 3/26 Again, convert to a common denominator (26):   3/13 = 6/26, 1/2 = 13/26 Thus:   P(F or E) = 6/26 + 13/26 − 3/26 = (6 + 13 − 3)/26 = 16/26 = 8/13 ────────────────────────────── Summary of Answers: a. 1/24 b. 3/8 c. 3/26 d. 8/13