Responses for Assignment Week 3 Chapter 11
1.
The Law of Large Numbers is a fundamental concept in probability and statistics. Simply
put, it states that as you collect more and more data, the average outcome will get closer
to the expected or true value. In other words, the more trials, or observations, the more
accurate the results become. This is why it's important to base conclusions on large
sample sizes, as they are more likely to represent the true situation.
2.
You will first need to know the expected theoretical probabilities for a fair die-6
You need to collect empirical data by rolling the die a sufficiently large number of times to
obtain a representative sample.
After obtaining the data, compute the empirical probability of
each side of the die by dividing the number of times each side appeared by the total number of
rolls.
P(1) = 100/600 = 1/6 ≈ 16.67%
P(2) = 100/600 = 1/6 ≈ 16.67%
P(3) = 100/600 = 1/6 ≈ 16.67%
P(4) = 100/600 = 1/6 ≈ 16.67%
P(5) = 100/600 = 1/6 ≈ 16.67%
P(6) = 100/600 = 1/6 ≈ 16.67%
3
. Empirical Probability = 40 / 45
Empirical Probability = 8 / 9 - The empirical probability that the next person who purchases a
phone from that store will buy a smartphone is 8/9 or approximately 0.89.
4.
To do this, we will first understand that there are 52 cards in a standard deck, with 13 cards in each
of the four suits - hearts, diamonds, clubs, and spades. Therefore, there are 13 hearts in the deck. The
probability of drawing a heart at any given draw is 13/52 or approximately 0.25. let's say we drew a heart
'x' times out of the 40 draws.
Empirical probability = x/40
6.
Probability = 5 even numbers / 10 total digits = 1/2 or 0.5
7.
P(odd or >3) = 5/10+6/10-3/10=8/10=4/5