The probability of the union of two events is the sum of their probability, minus the probability of their interserction:
![P(A \cup B) = P(A) + P(B) - P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28A%20%5Ccap%20B%29%20)
If we plug the known values into this formula, we have
![\dfrac{3}{5} = \dfrac{1}{3} + \dfrac{2}{5} - P(A\cap B)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B3%7D%7B5%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B2%7D%7B5%7D%20-%20P%28A%5Ccap%20B%29%20)
From which we can deduce
![P(A\cap B) = \dfrac{1}{3} + \dfrac{2}{5} - \dfrac{3}{5} = \dfrac{2}{15}](https://tex.z-dn.net/?f=%20P%28A%5Ccap%20B%29%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B2%7D%7B5%7D%20-%20%5Cdfrac%7B3%7D%7B5%7D%20%3D%20%5Cdfrac%7B2%7D%7B15%7D%20)
So, the probability of
is a bit less than
, we have to take away all events that belong to B as well:
![P(A \setminus B) = P(A) - P(A\cap B) = \dfrac{1}{3} - \dfrac{2}{15} = \dfrac{1}{5}](https://tex.z-dn.net/?f=%20P%28A%20%5Csetminus%20B%29%20%3D%20P%28A%29%20-%20P%28A%5Ccap%20B%29%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20-%20%5Cdfrac%7B2%7D%7B15%7D%20%3D%20%5Cdfrac%7B1%7D%7B5%7D)
Answer:
d
Step-by-step explanation:
Answer:
um what I do is I go from like if I was doing 12 I would go 1 times 12 and then 2 times 6 and 3 times 4 and then I would stop cause it's repetitive if that makes sense
Answer:
FV= 1,000*(1.12^n)
Step-by-step explanation:
Giving the following information:
Initial investment= $1,000
Increase rate= 12% = 0.12
We need to formulate an exponential equation to show the value in n years.
<u>To calculate the Future Value, we need to use the following formula:</u>
FV= PV*(1+i)^n
Being:
FV= Future Value
PV= Initial Investment
i= increase rate
n= number of periods
FV= 1,000*(1.12^n)
<u>For example, for one year:</u>
FV= 1,000*(1.12^1)
FV= $1,120
For 3 years:
FV= 1,000*(1.12^3)
FV= $1,404.93