please help.
what is the probability that when you pick two cards, you will select at least one king out of two in a deck of six standard cards? (assuming there are no jokers)
A deck of six cards?
Most decks have 52 cards.
its six out of the 52 but you pick two of the six and two out of the six cards are kings , I'm supposedto find out if its more likely to pick one king or none?
To find the probability of selecting at least one king out of two cards in a deck of six standard cards, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Possible Outcomes:
In a standard deck of playing cards, there are 52 cards. When we pick two cards, there are 52C2 = (52!)/(2!(52-2)!) = 1326 possible combinations of two cards.
Number of Favorable Outcomes:
To determine the number of favorable outcomes, we need to consider two scenarios:
1. Selecting one king and one non-king card.
2. Selecting both kings.
Scenario 1: Selecting one king and one non-king card:
There are 4 kings in a deck of cards. We need to select one king out of the 4 possible kings and one non-king card out of the remaining 48 non-king cards. Since we are selecting one card of each type, we need to multiply the number of choices for each category. Therefore, the favorable outcomes for this scenario are 4C1 * 48C1 = (4!)/(1!(4-1)!)(48!)/(1!(48-1)!) = 192.
Scenario 2: Selecting both kings:
There are 4 kings in a deck of cards, and we need to select 2 kings out of the 4 possible kings. We can calculate this combination using the formula 4C2 = (4!)/(2!(4-2)!) = 6.
Total Number of Favorable Outcomes:
To determine the total number of favorable outcomes, we add the outcomes from both scenarios: 192 favorable outcomes from scenario 1 + 6 favorable outcomes from scenario 2 = 198 favorable outcomes.
Now we can calculate the probability of selecting at least one king out of two cards:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = 198 / 1326
Probability ≈ 0.149 or 14.9%
Therefore, the probability of selecting at least one king out of two cards in a deck of six standard cards is approximately 14.9%.