A bag has 3 red marbles, 2 blue, 4 green and 1 yellow. What is the theoretical probability of pulling a red marble? Write your a
nswer as a fraction, decimal, and percent.
1 answer:
You might be interested in
To model this situation, we are going to use the decay formula: 
where
is the final pupolation
is the initial population
is the Euler's constant
is the decay rate
is the time in years
A. We know for our problem that the initial population is 1,250, so
; we also know that after a year the population is 1000, so 
and 
. Lets replace those values in our formula to find :
Now that we have, we can write a function to model this scenario:
.
B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.
C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
- Over the interval [0,10], the function will have a minimum at t=10:
D. To find the rate of change of the function over the interval [0,10], we are going to use the formula:
where
is the rate of change
is the function evaluated at 10
is the function evaluated at 0
We know from previous calculations that
and 
, so lets replace those values in our formula to find :
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.
where
A. We know for our problem that the initial population is 1,250, so
Now that we have
B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.
C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
- Over the interval [0,10], the function will have a minimum at t=10:
D. To find the rate of change of the function over the interval [0,10], we are going to use the formula:
where
We know from previous calculations that
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.
Answer:
The probability is
Step-by-step explanation:
From the question we are told that
The number of green marbles is
The number of red marbles is
The number of red marbles is
Generally the total number of marbles is mathematically represented as
Generally total number of marbles that are not red is
=>
=>
The probability of the first ball not being red is mathematically represented as
=>
The probability of the second ball not being red is mathematically represented as
=> (the subtraction is because the marbles where selected without replacement )
=>
The probability that the first two balls is not red is mathematically represented as
=>
=>
The probability of the third ball being red is mathematically represented as
(the subtraction is because the marbles where selected without replacement )
=>
Generally the probability of the first two marble not being red and the third marble being red is mathematically represented as
=>