Answer:
9.11*10^-4 %
Step-by-step explanation:
To find the probability, you simply need to find the possible outcomes that allows no rooks to be in danger, and the possible amount of ways to place the rooks.
For the first outcome, you start by putting 1 rook in the first columns, you have 8 possible rows to do this. The next rook in the next column will only have 7 possible rows, as you have to exclude the one where the previous rook is located. The next rook, 6 possibilities, the next 5, and so on. So we conclude that the total amount of ways so that none of the rooks can capture any of the other rooks is 8*7*6*5*4*3*2*1 = 8! = 40320
In order to find the total amount of ways to place the rooks, you can just use a combinatoric:
![\left[\begin{array}{ccc}64\\8\end{array}\right]= \frac{64!}{8!(64-8)!} = 4.43*10^9](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D64%5C%5C8%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cfrac%7B64%21%7D%7B8%21%2864-8%29%21%7D%20%3D%204.43%2A10%5E9)
Then:
P = 
We will see that the probability of picking two orange marbles without replacement is 0.23
<h3>
How to get the probability?</h3>
If we assume that all the marbles have the same probability of being randomly picked, then the probability of getting an orange marble is given by the quotient between the number of orange marbles and the total number of marbles, this gives:
P = 6/12 = 1/2
And then we need to get another orange marble, without replacing the one we picked before, this time there are 5 orange marbles and 11 in total, so the probability is:
Q = 5/11
Finally, the joint probability (of these two events happening) is the product of the probabilities, so we get:
P*Q = (1/2)*(5/11) = 0.23
If you want to learn more about probability, you can read:
brainly.com/question/251701
The volume of the balloon is 500 cubic inches after 20 seconds
<h3>How to determine the volume?</h3>
From the given graph, we have:
- Time on the x-axis
- Volume on the y-axis
Also from the graph, we have:
V(20) = 500
This means that:
The volume of the balloon is 500 cubic inches after 20 seconds
Read more about graphs at:
brainly.com/question/4025726
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Can I im see the graph pleaseeewww
