To determine the probability of selecting a heart or a 9 from a standard deck of 52 playing cards, we first need to consider how many favorable outcomes there are for each event.
There are 13 hearts in a deck. Additionally, there are 4 nines in the deck, one of which is a heart. Therefore, when we add the number of hearts and the number of nines, we need to subtract the overlap (the 9 of hearts) to avoid double counting.
Here’s the calculation step-by-step:
- Number of hearts = 13
- Number of nines = 4
- Overlapping card (9 of hearts) = 1
Using the principle of inclusion-exclusion, the total number of favorable outcomes is:
Favorable outcomes = Number of hearts + Number of nines – Overlapping card
Favorable outcomes = 13 + 4 – 1 = 16
Now, the probability of selecting a heart or a 9 is given by the ratio of favorable outcomes to the total number of outcomes:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 16 / 52
This fraction can be simplified:
Probability = 4 / 13
Therefore, the probability of drawing a heart or a 9 from a standard deck of cards is 4/13.