Answer:
![a.\frac{1}{13}\\b.\frac{1}{2}\\c.\frac{1}{13}\\d.\frac{1}{13}](https://tex.z-dn.net/?f=a.%5Cfrac%7B1%7D%7B13%7D%5C%5Cb.%5Cfrac%7B1%7D%7B2%7D%5C%5Cc.%5Cfrac%7B1%7D%7B13%7D%5C%5Cd.%5Cfrac%7B1%7D%7B13%7D)
Step-by-step explanation:
P(A|B) = P(A and B) / P(B)
Total number of cards = 52
a)
Let A denotes the event that the card is a diamond and B denotes the card is red.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}\\=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%5C%5C%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B52%7D%7D%7B%5Cfrac%7B26%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B13%7D)
b)
Let A denotes the event that the card is red and B denotes the card is diamond.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{4}{52}}\\=\frac{1}{2}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B52%7D%7D%7B%5Cfrac%7B4%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
c)
Let A denotes the event that the card is nine and B denotes the card is red.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B52%7D%7D%7B%5Cfrac%7B26%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B13%7D)
d)
Let A denotes the event that the card is a king and B denotes the card is a face card.
![P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{4}{52}}{\frac{12}{52}}\\=\frac{1}{13}](https://tex.z-dn.net/?f=P%5Cleft%20%28%20A%7CB%20%5Cright%20%29%3D%5Cfrac%7BP%5Cleft%20%28%20A%5Ccap%20B%20%5Cright%20%29%7D%7BP%28B%29%7D%3D%5Cfrac%7B%5Cfrac%7B4%7D%7B52%7D%7D%7B%5Cfrac%7B12%7D%7B52%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B13%7D)
The estimate to 4 x 979 is 4 x 1,000. The answer is 3,916
Answer:
D) 89.6 %
Average or mean of the given data = 89.6 %
Step-by-step explanation:
<em><u>Step(i):-</u></em>
Given data
X : 82 100 84
P(X=x) : 0.40 0.40 0.20
<u><em>Step(ii)</em></u>
Let 'X' be the discrete distribution
Mean of the discrete distribution = ∑ x P( x=x)
= 82 ×0.40 +100 ×0.40 +84 ×0.20
= 89.6
<u><em>Final answer:-</em></u>
Average of the given data = 89.6 %
Answer:
25
Step-by-step explanation:
if you look at it, 250 is 1/4 of 1000 and 100 is 1/10 of 1000 so divide 250 by 10 and you get your answer.