Find the probability of drawing number less than 5 or a number greater than 7 from a deck of 52 cards. (Reminder: playing cards have numbers between 2 and 10, inclusive)
there are 12 cards that are 5 through 7 ... 4 suits
p = (52 - 12) / 52
To find the probability of drawing a number less than 5 or a number greater than 7 from a deck of 52 cards, we first need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable outcomes:
- The numbers less than 5 are 2, 3, and 4. Each number has 4 different suits, so there are a total of 4 × 3 = 12 favorable outcomes for numbers less than 5.
- The numbers greater than 7 are 8, 9, and 10. Again, each number has 4 different suits, so there are a total of 4 × 3 = 12 favorable outcomes for numbers greater than 7.
Total number of possible outcomes:
Since there are 52 cards in a deck, the total number of possible outcomes is 52.
Now we can calculate the probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = (12 + 12) / 52
Probability = 24 / 52
Simplifying the fraction:
Probability = 6 / 13
Therefore, the probability of drawing a number less than 5 or a number greater than 7 from a deck of 52 cards is 6/13.