If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a Queen or 5?
4 queens or 4 fives
prob(of stated event) = 8/52 = 2/13
To find the probability of selecting a Queen or a 5 from a standard deck of 52 cards, we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Number of favorable outcomes:
There are 4 Queens in a deck, and there are also 4 Fives. However, we need to be careful not to count the Queen of Hearts and the Five of Hearts twice, as these cards fall into both categories. So, the number of favorable outcomes is 4 (the Queens) + 4 (the Fives) - 2 (the Queen of Hearts and the Five of Hearts) = 6.
2. Total number of possible outcomes:
In a standard deck, there are 52 cards.
Therefore, the probability of randomly selecting a Queen or a 5 is:
Number of favorable outcomes / Total number of possible outcomes
6 / 52 = 3 / 26.
So, the probability is 3/26.
To determine the probability of randomly selecting a Queen or a 5 from a well-shuffled standard deck of 52 cards, we first need to find the number of favorable outcomes (cards that are either a Queen or a 5) and the total number of possible outcomes (the entire deck of 52 cards).
There are 4 Queens in a deck (one for each suit - Hearts, Diamonds, Clubs, and Spades) and 4 fives as well. Since there is no overlap between the sets of Queens and fives, the total number of favorable outcomes is 4 (Queens) + 4 (fives) = 8.
The total number of possible outcomes is the number of cards in the deck, which is 52.
Therefore, the probability of randomly selecting a Queen or a 5 can be calculated as:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 8 / 52
Simplifying the fraction, we get:
Probability = 2 / 13
So, the probability that the card you select is a Queen or a 5 is 2/13.