MATH 211 Week 4 Discussion | Embry Riddle Aeronautical University | Assignment Help
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- 04 May 2021
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MATH 211 Week 4 Discussion | Embry Riddle Aeronautical University | Assignment Help
Module 4 - Discussion:
Relative Frequency Approximation of Probability
Probability
This discussion activity will familiarize you with
probability using an applet. The applet is a simulation of flipping a fair coin
a given number of times and then estimating the probability of getting a head
using the relative frequency approximation of probability.
The probability of getting a head or
tail on one flip of a fair coin is 0.5 or 50%. The relative frequency
approximation of probability says that the probability of an Event A
is estimated by dividing the number of times that Event A occurred by the
number of times the trial was repeated. For example, if you flip a coin 10
times and get 4 heads, then you could estimate the probability of getting a
head as 4 divided by 10 or 0.4.
Run Applet & Reflect
Use the Simulating the probability of a
head (with a fair coin) (Links to an external
site.) applet and follow steps 1 through 5.
1.
At the top left side of
the applet, under “Coin Flipping”, select “5 flips”. After the simulation
finishes the 5 flips, select “5 flips” again for a total of 10 flips
of the coin. Record the number of heads (given in the box labeled Count) in 10
flips of a coin and the cumulative probability of a head based on the ten
flips. (The cumulative probability is given in the box labeled Proportion.) Is
the number of heads what you expected in 10 flips?
2.
Now select 5 flips
four more times (you will need to wait for each 5 flips to complete before
clicking again.) You should now have 30 flips of the coin (see the Total
column). Record the number of heads in 30 flips and the cumulative probability
of a head based on 30 flips. What is the longest string of consecutive heads or
tails that you got in the 30 flips? Do you think that is unusual? (In the Flips
box you can use the scroll bar to look at the individual coins to find
consecutive heads or tails. You can also select the box labeled
“Convergence” to locate consecutive strings. When you flip heads the line rises
and when you flip tails the line falls.)
3.
Now select 1000
flips. This should give you 1030 flips of the coin. Record the number of heads
and the cumulative probability of a head now.
4.
Select 1000 flips one
more time so that you have 2030 flips. Record the number of heads and the
cumulative probability of a head now.
5.
“The Law of Large Numbers
states that if an experiment with a random outcome is repeated a large number
of times, the empirical probability of an event is likely to be close to the
true probability. The larger the number of repetitions, the closer together
these probabilities are likely to be” (Text, p. 224). Does the coin flipping
process you just completed illustrate the Law of Large Numbers? Why or why not?
Post
Share your results and reflections from the five steps of
the applet activity.