Math Problem Statement

If one card is drawn from a deck, find the probability of getting these results. (a) A club or a heart

Solution

The problem asks to find the probability of drawing either a club or a heart from a standard deck of 52 cards.

Step-by-Step Solution:

  1. A standard deck of cards contains:

    • 4 suits: Clubs, Diamonds, Hearts, Spades.
    • 13 cards per suit.
  2. To find P(club or heart)P(\text{club or heart}), we need the number of favorable outcomes (either a club or a heart) and divide it by the total number of cards.

    • There are 13 clubs.
    • There are 13 hearts.
  3. Since there is no overlap (a card cannot be both a club and a heart), the total number of favorable outcomes is: 13(clubs)+13(hearts)=26favorable outcomes.13 \, (\text{clubs}) + 13 \, (\text{hearts}) = 26 \, \text{favorable outcomes}.

  4. The probability is: P(club or heart)=2652=12=0.500.P(\text{club or heart}) = \frac{26}{52} = \frac{1}{2} = 0.500.

Thus, the probability P(club or heart)P(\text{club or heart}) is 0.500.

Would you like to go into more detail, or do you have any questions?


Here are 5 related questions to explore:

  1. What is the probability of drawing a spade or a diamond?
  2. What is the probability of drawing a face card (Jack, Queen, or King)?
  3. What is the probability of drawing an ace from the deck?
  4. How does the probability change if we exclude jokers from a 54-card deck?
  5. What is the probability of drawing a red card (hearts or diamonds)?

Tip: When calculating probabilities for "or" events, ensure you account for any overlap between events, if applicable.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Card Combinatorics

Formulas

P(event) = (Number of favorable outcomes) / (Total number of possible outcomes)
P(club or heart) = P(club) + P(heart) - P(club and heart)

Theorems

Addition Rule for Probability

Suitable Grade Level

Grades 7-10