Determine the probability that the single card drawn from a standard 52-card deck is a four, a five, or a spade. Illustrate the probabilities using a Venn Diagram
Either-or probabilities are found by adding the individual probabilities.
Out of 52-card deck, there are four 4s, four 5s and 13 spades. However, 2 of the spades are a 4 and a 5.
Can you work it from there?
To determine the probability that the single card drawn from a standard 52-card deck is a four, a five, or a spade, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Count the favorable outcomes
- There are four fours and four fives in a deck of cards.
- There are 13 spades in a deck of cards (one for each rank).
Step 2: Count the total number of possible outcomes
- A standard 52-card deck consists of four suits (spades, hearts, diamonds, and clubs) with 13 ranks in each suit.
Step 3: Calculate the probability
- Probability = (Number of favorable outcomes) / (Number of total outcomes)
- P(Four or Five or Spade) = (4 + 4 + 13) / 52
= 21 / 52
= 0.404 or 40.4% (approximately)
Now, let's illustrate these probabilities using a Venn diagram.
**Venn Diagram**
1) Draw a rectangle to represent the sample space, which consists of 52 cards.
2) Draw three overlapping circles inside the rectangle to represent the three events: "Four," "Five," and "Spade."
3) Label the circles accordingly.
4) The "Four" circle contains four elements: four-of-spades, four-of-hearts, four-of-diamonds, and four-of-clubs.
5) The "Five" circle contains four elements: five-of-spades, five-of-hearts, five-of-diamonds, and five-of-clubs.
6) The "Spade" circle contains 13 elements: all the spades in the deck.
7) The overlapping regions represent the cards that belong to multiple events (e.g., cards that are both "Four" and "Spade").
8) The probability of an event is determined by the fraction of the sample space it occupies.