A 3-card poker hand is dealt at random from a standard 52-card deck. What is the total number of possible hands? What is the tot
1 answer:
Answer:
What is the total number of possible hands?
For this case n = 52 and x =3 and if we replace we got:
So then we have a total of 22100 ways in order to select 3 cards from a total of 52 cards.
What is the total number of possible hands if the hand contains exactly one heart?
For the possible cases we can do this:
Since we have 13 hearts and we want to select 1 and the two remain cards are non hearts. So we have 9633 ways in order to have only one heart in a hand of 3, and the probability would be:
Step-by-step explanation:
What is the total number of possible hands?
For this case we assume that w ehave an standard deck of 52 cards and we want to know on how many ways we can select 3 cards from the total of 52, so for this case since the order no matter we can use the formula for combination given by:
For this case n = 52 and x =3 and if we replace we got:
So then we have a total of 22100 ways in order to select 3 cards from a total of 52 cards.
What is the total number of possible hands if the hand contains exactly one heart?
For this case we need to remember that in a tandard deck we have 13 hearts and we want that in the 3 selected card we have just one heart, and we can find this probability using the definition of empirical probability:
Where the total cases on this case are 22100
For the possible cases we can do this:
Since we have 13 hearts and we want to select 1 and the two remain cards are non hearts. So we have 9633 ways in order to have only one heart in a hand of 3, and the probability would be:
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A square has 4 equal sides, which means when you need to work out the area, you're doing length × width, but the length and width are exactly the same, because it's a square (look at the picture if you don't understand this).
That means you just have to pick any side (let's call this side x), and multiply it by another side of the square. Now, because all of the sides are equal, you're doing x multiplied by x, which is the same as x².
Therefore, if the area is equal to x², and in this question, it's also equal to 49 (as stated in the question), we can equate them to each other:
x² = 49
Now to get the x by itself, we need to do the opposite of squaring, which is square rooting. Therefore, we square root both sides of the equation:
√x² = √49
The √ and the ² cancel out, so you're just left with x:
x = √49
The square root of 49 is just 7, so we can replace √49 with 7, and we get:
x = 7
Now remember, earlier, I called x the value of one side. Therefore, by remembering that, you know that the value of one side is equal to 7. And because all the sides are the same as each other, each side is equal to 7 metres.
Therefore, your final answer is 7 metres :)
