The student will use theoretical and empirical methods to estimate probabilities.
The student will appraise the differences between the two estimates.
The student will demonstrate an understanding of long-term relative frequencies.
Do the experiment
Count out 40 mixed-color M&Ms® which is approximately one small bag’s worth. Record the number of each color in
[link] . Use the information from this table to complete
[link] . Next, put the M&Ms in a cup. The experiment is to pick two M&Ms, one at a time. Do
not look at them as you pick them. The first time through, replace the first M&M before picking the second one. Record the results in the “With Replacement” column of
[link] . Do this 24 times. The second time through, after picking the first M&M, do
not replace it before picking the second one. Then, pick the second one. Record the results in the “Without Replacement” column section of
[link] . After you record the pick, put
both M&Ms back. Do this a total of 24 times, also. Use the data from
[link] to calculate the empirical probability questions. Leave your answers in unreduced fractional form. Do
not multiply out any fractions.
Population
Color
Quantity
Yellow (
Y )
Green (
G )
Blue (
BL )
Brown (
B )
Orange (
O )
Red (
R )
Theoretical probabilities
With Replacement
Without Replacement
P (2 reds)
P (
R1B2 OR
B1R2 )
P (
R1 AND
G2 )
P (
G2 |
R1 )
P (no yellows)
P (doubles)
P (no doubles)
Note
G2 = green on second pick;
R1 = red on first pick;
B1 = brown on first pick;
B2 = brown on second pick; doubles = both picks are the same colour.
Empirical results
With Replacement
Without Replacement
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
Empirical probabilities
With Replacement
Without Replacement
P (2 reds)
P (
R1B2 OR
B1R2 )
P (
R1 AND
G2 )
P (
G2 |
R1 )
P (no yellows)
P (doubles)
P (no doubles)
Discussion questions
Why are the “With Replacement” and “Without Replacement” probabilities different?
Convert
P (no yellows) to decimal format for both Theoretical “With Replacement” and for Empirical “With Replacement”. Round to four decimal places.
Theoretical “With Replacement”:
P (no yellows) = _______
Empirical “With Replacement”:
P (no yellows) = _______
Are the decimal values “close”? Did you expect them to be closer together or farther apart? Why?
If you increased the number of times you picked two M&Ms to 240 times, why would empirical probability values change?
Would this change (see part 3) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? How do you know?
Explain the differences in what
P (
G1 AND
R2 ) and
P (
R1 |
G2 ) represent. Hint: Think about the sample space for each probability.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
