There are 4 aces and 4 kings in a standard deck of 52 cards. You pick one card at random. What is the probability of selecting an ace or a king? Explain your reasoning.
I am a bit confused on this one. Please help.
Hello. I think I just figured this out.
The odds of picking an ace or a king is:
8/52 (since there are 4 aces and 4 kings in a single deck, 4+4=8_
8/52 can be simplified to 2/13
Answer=2/13
Hello Reiny: I am confused on prob(not ace or king)
How do you actually go about figuring this out and can you explain this so I have a better understanding.
Thank you
You are interested in 8 cards from 52 cards, so .....
Don't confuse "odds" with "probability", they are not the same thing
You are right, the prob(king or ace) = 2/13
the odds in favour of "a king or ace) = prob(ace or king) : prob(not ace or king)
= (2/13) : (11/13)
= 2 : 11
In general, if the prob(some event happening) = q
then the prob(of the event NOT happening) = 1 - q
then you use these in the definition of "odds"
To find the probability of selecting an ace or a king from a standard deck of 52 cards, you need to calculate the number of favorable outcomes (ace or king) and divide it by the total number of possible outcomes (52 cards).
In a standard deck, there are 4 aces and 4 kings. So the number of favorable outcomes, which is the number of aces plus the number of kings, is 4 + 4 = 8.
The total number of possible outcomes is 52, because there are 52 cards in a standard deck.
Therefore, the probability of selecting an ace or a king is calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 8 / 52
Simplifying the fraction, you get:
Probability = 2 / 13
So the probability of selecting an ace or a king from a standard deck is 2/13.
To find the probability, you can also think of it as dividing the number of ways to select an ace or a king by the total number of possible card selections. In this case, there are 8 ways to select an ace or a king (4 aces + 4 kings) and 52 ways to select any card from the deck. Hence, the probability is 8/52, which simplifies to 2/13.