Answer:
The probability is 0.0052
Step-by-step explanation:
Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:
P(A/B) = P(A∩B)/P(B)
The probability P(B) that at least three are aces is the sum of the following probabilities:
- The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
- There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:
![nCk=\frac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=nCk%3D%5Cfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D)
So, the number of ways to select exactly 3 aces is:
![4C3*48C1=\frac{4!}{3!(4-3)!}*\frac{48!}{1!(48-1)!}=192](https://tex.z-dn.net/?f=4C3%2A48C1%3D%5Cfrac%7B4%21%7D%7B3%21%284-3%29%21%7D%2A%5Cfrac%7B48%21%7D%7B1%21%2848-1%29%21%7D%3D192)
Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725
Then, the probability P(B) that at least three are aces is:
![P(B)=\frac{1}{270,725} +\frac{192}{270,725} =\frac{193}{270,725}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7B1%7D%7B270%2C725%7D%20%2B%5Cfrac%7B192%7D%7B270%2C725%7D%20%3D%5Cfrac%7B193%7D%7B270%2C725%7D)
On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:
P(A∩B) = 1/270,725
Finally, the probability P(A/B) that all four are aces given that at least three are aces is:
![P=\frac{1/270,725}{193/270,725} =\frac{1}{193}=0.0052](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%2F270%2C725%7D%7B193%2F270%2C725%7D%20%3D%5Cfrac%7B1%7D%7B193%7D%3D0.0052)
Answer:
if it asking for the type of angle the both are obtuse and the fisrt measure is 135 and the second is 101
Step-by-step explanation:
I think that it is 0.035 or 3/100
Answer:
124250cm, 1242.5m or 1.2425km
Step-by-step explanation:
0.6% = 6/100
6/100 = 0.006
0.006*1.25 = 0.0075
1.25km = 1250m = 125000cm
0.0075km = 7.5m = 750cm
125000 - 750 = 124250
Therefore:
The answer is 124250cm, 1242.5m or 1.2425km
Sub to oTechz :)
2 times the square root of 5 . that’s what i got .