Understanding Probability with a Deck of Cards
Probability is the measure of the likelihood that an event will occur. In mathematics, the probability of an event $E$ is given by the formula:
$$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
A standard deck of playing cards contains 52 unique cards, which serves as our total sample space ($n = 52$).
Solving the Problems
(i) Probability of drawing a red card
- Total outcomes: 52
- Favorable outcomes: There are two red suits in a deck: Hearts and Diamonds. Each suit has 13 cards. Thus, total red cards = $13 + 13 = 26$.
- Calculation: $$P(\text{Red Card}) = \frac{26}{52} = \frac{1}{2} = 0.5$$
(ii) Probability of drawing a heart
- Total outcomes: 52
- Favorable outcomes: There are four suits in a deck: Hearts, Diamonds, Clubs, and Spades. Each suit has exactly 13 cards.
- Calculation: $$P(\text{Heart}) = \frac{13}{52} = \frac{1}{4} = 0.25$$
Key Takeaways
- Always identify the total number of outcomes first.
- Break down the categories within the deck (Suits vs. Colors).
- Simplify your final fraction to its lowest terms for clarity.