To find the probability of selecting a heart or an 8 from a standard deck of 52 playing cards, we need to consider both the total number of favorable outcomes and the total number of possible outcomes.
Firstly, let’s identify the total number of hearts in a deck. There are 13 hearts in a standard deck. Next, we also have to account for the eights. There is one 8 of hearts, but besides that, there are also 8 of diamonds, 8 of clubs, and 8 of spades, making a total of 4 eights in the deck.
Now, if we simply add the hearts and the eights together, we might mistakenly count the 8 of hearts twice. So, we have:
- Number of hearts = 13
- Number of eights = 4
- 8 of hearts (which is already counted as a heart) = 1
Using the principle of inclusion-exclusion to avoid double counting, the total number of favorable outcomes is:
Favorable outcomes = Number of hearts + Number of eights – Number of 8 of hearts
Favorable outcomes = 13 + 4 – 1 = 16
Now, the probability of drawing a heart or an 8 can be calculated using the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 16 / 52
To simplify this fraction, we can divide both the numerator and the denominator by 4:
Probability = 4 / 13
Therefore, the probability of selecting a heart or an 8 from a standard deck of cards is 4/13.