Let x be the percent of p asked
then
m% of n = x% of p
m/100*n = x/100*p
mn = xp
x = mn/p
Answer:
20 x
Step-by-step explanation:
i hope that is it
5x^2 - 24x + 8 is your answer to this equation
Answer:
Part A:
The probability that all of the balls selected are white:
![P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B1%7D%7B6%7D%28%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B21%7D%2B%5Cfrac%7B2%7D%7B91%7D%2B%5Cfrac%7B1%7D%7B273%7D%2B%5Cfrac%7B1%7D%7B3003%7D%2B0%29%5C%5C%20%20%20%20%20%20P%28A%29%3D%5Cfrac%7B5%7D%7B66%7D%3D0.075757576)
Part B:
The conditional probability that the die landed on 3 if all the balls selected are white:
![P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516](https://tex.z-dn.net/?f=P%28D_3%7CA%29%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B91%7D%2A%5Cfrac%7B1%7D%7B6%7D%7D%7B%5Cfrac%7B5%7D%7B66%7D%20%7D%20%5C%5CP%28D_3%7CA%29%3D%5Cfrac%7B22%7D%7B455%7D%3D0.0483516)
Step-by-step explanation:
A is the event all balls are white.
D_i is the dice outcome.
Sine the die is fair:
for i∈{1,2,3,4,5,6}
In case of 10 black and 5 white balls:
![P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%7CD_1%29%3D%5Cfrac%7B5_%7BC%7D_1%7D%7B15_%7BC%7D_1%7D%20%3D%5Cfrac%7B5%7D%7B15%7D%3D%5Cfrac%7B1%7D%7B3%7D)
![P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}](https://tex.z-dn.net/?f=P%28A%7CD_2%29%3D%5Cfrac%7B5_%7BC%7D_2%7D%7B15_%7BC%7D_2%7D%20%3D%5Cfrac%7B10%7D%7B105%7D%3D%5Cfrac%7B2%7D%7B21%7D)
![P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}](https://tex.z-dn.net/?f=P%28A%7CD_3%29%3D%5Cfrac%7B5_%7BC%7D_3%7D%7B15_%7BC%7D_3%7D%20%3D%5Cfrac%7B10%7D%7B455%7D%3D%5Cfrac%7B2%7D%7B91%7D)
![P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}](https://tex.z-dn.net/?f=P%28A%7CD_4%29%3D%5Cfrac%7B5_%7BC%7D_4%7D%7B15_%7BC%7D_4%7D%20%3D%5Cfrac%7B5%7D%7B1365%7D%3D%5Cfrac%7B1%7D%7B273%7D)
![P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}](https://tex.z-dn.net/?f=P%28A%7CD_5%29%3D%5Cfrac%7B5_%7BC%7D_5%7D%7B15_%7BC%7D_5%7D%20%3D%5Cfrac%7B1%7D%7B3003%7D%3D%5Cfrac%7B1%7D%7B3003%7D)
![P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0](https://tex.z-dn.net/?f=P%28A%7CD_6%29%3D%5Cfrac%7B5_%7BC%7D_6%7D%7B15_%7BC%7D_6%7D%20%3D0)
Part A:
The probability that all of the balls selected are white:
![P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)](https://tex.z-dn.net/?f=P%28A%29%3D%5Csum%5E6_%7Bi%3D1%7D%20P%28A%7CD_i%29P%28D_i%29)
![P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B1%7D%7B6%7D%28%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B21%7D%2B%5Cfrac%7B2%7D%7B91%7D%2B%5Cfrac%7B1%7D%7B273%7D%2B%5Cfrac%7B1%7D%7B3003%7D%2B0%29%5C%5C%20%20%20%20%20%20P%28A%29%3D%5Cfrac%7B5%7D%7B66%7D%3D0.075757576)
Part B:
The conditional probability that the die landed on 3 if all the balls selected are white:
We have to find ![P(D_3|A)](https://tex.z-dn.net/?f=P%28D_3%7CA%29)
The data required is calculated above:
![P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516](https://tex.z-dn.net/?f=P%28D_3%7CA%29%3D%5Cfrac%7BP%28A%7CD_3%29P%28D_3%29%7D%7BP%28A%29%7D%5C%5C%20P%28D_3%7CA%29%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B91%7D%2A%5Cfrac%7B1%7D%7B6%7D%7D%7B%5Cfrac%7B5%7D%7B66%7D%20%7D%20%5C%5CP%28D_3%7CA%29%3D%5Cfrac%7B22%7D%7B455%7D%3D0.0483516)
Answer:
Step-by-step explanation:
Hope it helped u