Probability of a single draw

Goal: Write probabilities as counts ÷ total and use the complement and addition rules.

Remember: P(event) = outcomes in the event ÷ total equally likely outcomes. P(not A) = 1 − P(A).

1. 1.A card is drawn from a full deck. What is the probability it is a heart?

   Answer: 13/52 = 1/4 = 25%

2. 2.What is the probability it is an ace?

   Answer: 4/52 = 1/13 ≈ 7.69%

3. 3.What is the probability it is a face card (J, Q or K)?

   Answer: 12/52 = 3/13 ≈ 23.08%

4. 4.What is the probability it is a heart or a king? (Careful: one card is both.)

   Answer: 16/52 = 4/13 ≈ 30.77%

   Working: 13/52 + 4/52 − 1/52

5. 5.What is the probability it is a red number card from 2 to 10?

   Answer: 18/52 = 9/26 ≈ 34.62%

   Working: 9 ranks × 2 red suits = 18 cards

6. 6.What is the probability it is not a spade?

   Answer: 39/52 = 75%

   Working: 1 − 13/52

7. 7.Two cards are drawn in a row without replacement. What is the probability both are aces?

   Answer: 1/221 ≈ 0.45%

   Working: 4/52 × 3/51 = 12/2,652

8. 8.Why is the second fraction 3/51 and not 4/52?

   Answer: One ace has already been removed, so 3 aces remain among 51 cards.