What is the number of favourable outcomes when determining the probability of getting a King or a Heart greater than 10?
Understand the Problem
The question is asking about calculating the number of favorable outcomes when determining the probability of drawing either a King or a Heart card that has a value greater than 10 from a standard deck of playing cards. This requires analyzing the deck to find cards that meet the criteria.
Answer
$6$
Answer for screen readers
The total number of favorable outcomes is $6$.
Steps to Solve
- Identify the total number of cards in a standard deck
A standard deck of playing cards has a total of 52 cards.
- Identify the Kings in the deck
There are 4 Kings in a deck (one for each suit: hearts, diamonds, clubs, and spades).
- Identify the Hearts greater than 10
In a deck, the cards that have a value greater than 10 are the Jack, Queen, and King. As we already counted the King of Hearts amongst the Kings, we will only count the Jack and Queen of Hearts. So there are 2 Hearts (Jack and Queen).
- Sum the favorable outcomes
Now, we need to sum the total number of favorable outcomes which are:
- 4 Kings
- 2 Hearts greater than 10 (Jack and Queen of Hearts)
This gives us: $$ \text{Total favorable outcomes} = 4 + 2 = 6 $$
The total number of favorable outcomes is $6$.
More Information
In a deck of playing cards, the cards that can contribute to this scenario are specially selected Kings and specific Hearts. This exercise combines concepts of probability and counting distinct outcomes.
Tips
- Confusing the total number of cards with favorable outcomes.
- Failing to correctly assess which cards belong to two categories (like the King of Hearts being counted twice).
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