To calculate the probability of drawing a heart or a 9 from a deck of cards, we first need to understand the composition of a standard deck. A full deck contains 52 cards, which are split into 4 suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Among these, there are also 4 cards that are 9s (one from each suit).
Now, let’s break down the components:
- Number of hearts in the deck: 13
- Number of 9s in the deck: 4 (9 of hearts, 9 of diamonds, 9 of clubs, 9 of spades)
However, one card is counted twice in our calculation – the 9 of hearts. To find the total favorable outcomes, we can use the principle of inclusion-exclusion:
So, the total number of favorable outcomes is:
- Number of hearts + Number of 9s – Number of overlaps (9 of hearts)
- Thus, total = 13 + 4 – 1 = 16
Now, we can determine the probability. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
So, the probability of drawing a heart or a 9 is:
Probability = Favorable Outcomes / Total Outcomes = 16 / 52
This fraction can be simplified:
Probability = 4 / 13
Therefore, the probability of selecting a heart or a 9 when drawing a single card from a standard deck is 4/13, or approximately 0.3077, which is about 30.77%.