Mathematics
Mathematics
Problem
A card is drawn at random from a well-shuffled standard deck of 52 playing cards. a. (i) What is meant by the complementary event of a given event in probability theory? b. (ii) List the complementary event to “the card drawn is a heart.” c. (iii) Calculate the probability that the card drawn is not a heart. d. (iv) Verify that the probabilities of an event and its complement always add up to 1 for this situation.Intuitive explanation
When you draw one card from a full deck, you're working with basic probability: the chance of any single outcome is the ratio of favorable outcomes to total possible outcomes. The key insight is that a standard deck has a fixed composition—4 suits, 13 ranks—so you can count exactly how many cards match your target condition. Once you know that count, divide by 52 to get your probability.
Intuitive explanation
When you draw one card from a full deck, you're working with basic probability: the chance of any single outcome is the ratio of favorable outcomes to total possible outcomes. The key insight is that a standard deck has a fixed composition—4 suits, 13 ranks—so you can count exactly how many cards match your target condition. Once you know that count, divide by 52 to get your probability.