Exercise 1: Hearts and Face Cards, With the Union Rule — Possible Solution
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GIVEN
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A standard 52-card deck.
Event A = "drawing a heart" (13 cards)
Event B = "drawing a face card" (Jack, Queen, King - 12 cards total,
3 per suit)

STEP 1: P(A) AND P(B)
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P(A) = 13/52 = 1/4
P(B) = 12/52 = 3/13

STEP 2: P(A AND B)
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The overlap is the hearts that are ALSO face cards: the Jack, Queen,
and King of hearts - exactly 3 cards.

P(A and B) = 3/52

STEP 3: APPLYING THE UNION RULE
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P(A or B) = P(A) + P(B) - P(A and B)
          = 13/52 + 12/52 - 3/52
          = 22/52
          = 11/26

STEP 4: CONFIRMING BY DIRECT COUNT
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Cards satisfying "heart or face card": all 13 hearts, plus every face
card that ISN'T a heart (12 total face cards - 3 heart face cards =
9 non-heart face cards).

  13 + 9 = 22 cards out of 52

22/52 = 11/26, matching the union-rule result exactly.

WHY THIS WORKS AS AN ANSWER
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The union rule is applied using this chapter's own formula, correctly
identifying and subtracting the 3-card overlap between hearts and
face cards rather than double-counting them, and the result is
independently confirmed by directly counting the qualifying cards
rather than trusting the formula alone.