Answer:
Step-by-step explanation:
The team draws with a probability of 1 = (0.5 + 0.2) = 0.3
If the team does not win then it loses or draws.
Loosing = 0.2
Draw := 0.3
P(not win) = 0.2 + 0.3 = 0.5
======================
Not lose means wins or draws.
P(not lose) = 0.5 + 0.3 = 0.8
======================
Not Draw means wins or loses
P(not draw) = 0.5 + 0.2 = 0.7
Of course all of these could be done more directly.
P(not win)= (1 - win) = 1- 0.5 = 0.5
P(not lose) = ( 1 - lose) = 1 - 0.2 = 0.8
P(not draw) = (1 - 0.3) = 0.7
Answer:
(1,1)
Step-by-step explanation:
Answer:
B.63 and A. 36
Step-by-step explanation:
Answer:
![P(Same)=\frac{61}{190}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B61%7D%7B190%7D)
Step-by-step explanation:
Given
![Red = 5](https://tex.z-dn.net/?f=Red%20%3D%205)
![White = 6](https://tex.z-dn.net/?f=White%20%3D%206)
![Black = 9](https://tex.z-dn.net/?f=Black%20%3D%209)
Required
The probability of selecting 2 same colors when the first is not replaced
The total number of ball is:
![Total = 5 + 6 + 9](https://tex.z-dn.net/?f=Total%20%3D%205%20%2B%206%20%2B%209)
![Total = 20](https://tex.z-dn.net/?f=Total%20%3D%2020)
This is calculated as:
![P(Same)=P(Red\ and\ Red) + P(White\ and\ White) + P(Black\ and\ Black)](https://tex.z-dn.net/?f=P%28Same%29%3DP%28Red%5C%20and%5C%20Red%29%20%2B%20P%28White%5C%20and%5C%20White%29%20%2B%20P%28Black%5C%20and%5C%20Black%29)
So, we have:
![P(Same)=\frac{n(Red)}{Total} * \frac{n(Red) - 1}{Total - 1} + \frac{n(White)}{Total} * \frac{n(White) - 1}{Total - 1} + \frac{n(Black)}{Total} * \frac{n(Black) - 1}{Total - 1}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7Bn%28Red%29%7D%7BTotal%7D%20%2A%20%5Cfrac%7Bn%28Red%29%20-%201%7D%7BTotal%20-%201%7D%20%2B%20%5Cfrac%7Bn%28White%29%7D%7BTotal%7D%20%2A%20%5Cfrac%7Bn%28White%29%20-%201%7D%7BTotal%20-%201%7D%20%20%2B%20%5Cfrac%7Bn%28Black%29%7D%7BTotal%7D%20%2A%20%5Cfrac%7Bn%28Black%29%20-%201%7D%7BTotal%20-%201%7D)
<em>Note that: 1 is subtracted because it is a probability without replacement</em>
![P(Same)=\frac{5}{20} * \frac{5 - 1}{20- 1} + \frac{6}{20} * \frac{6 - 1}{20- 1} + \frac{9}{20} * \frac{9- 1}{20- 1}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B5%7D%7B20%7D%20%2A%20%5Cfrac%7B5%20-%201%7D%7B20-%201%7D%20%2B%20%5Cfrac%7B6%7D%7B20%7D%20%2A%20%5Cfrac%7B6%20-%201%7D%7B20-%201%7D%20%20%2B%20%5Cfrac%7B9%7D%7B20%7D%20%2A%20%5Cfrac%7B9-%201%7D%7B20-%201%7D)
![P(Same)=\frac{5}{20} * \frac{4}{19} + \frac{6}{20} * \frac{5}{19} + \frac{9}{20} * \frac{8}{19}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B5%7D%7B20%7D%20%2A%20%5Cfrac%7B4%7D%7B19%7D%20%2B%20%5Cfrac%7B6%7D%7B20%7D%20%2A%20%5Cfrac%7B5%7D%7B19%7D%20%20%2B%20%5Cfrac%7B9%7D%7B20%7D%20%2A%20%5Cfrac%7B8%7D%7B19%7D)
![P(Same)=\frac{20}{380} + \frac{30}{380} + \frac{72}{380}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B20%7D%7B380%7D%20%2B%20%5Cfrac%7B30%7D%7B380%7D%20%20%2B%20%5Cfrac%7B72%7D%7B380%7D)
![P(Same)=\frac{20+30+72}{380}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B20%2B30%2B72%7D%7B380%7D)
![P(Same)=\frac{122}{380}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B122%7D%7B380%7D)
![P(Same)=\frac{61}{190}](https://tex.z-dn.net/?f=P%28Same%29%3D%5Cfrac%7B61%7D%7B190%7D)
Answer:
(- 1, 1 ) and (2, 4 )
Step-by-step explanation:
Given the 2 equations
y = x + 2 → (1)
y = x² → (2)
Substitute y = x² into (1)
x² = x + 2 ( subtract x + 2 from both sides )
x² - x - 2 = 0 ← in standard form
(x - 2)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 2 → y = 2 + 2 = 4 ⇒ (2, 4 )
x = - 1 → y = - 1 + 2 = 1 ⇒ (- 1, 1 )