# Responses for Assignment Week 3 -

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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
8. There are 10 numbers in the hat in total. Since all the original numbers fulfill the given condition, the probability that the number selected is greater than 2 or less than 6 is 10/10 or simply 1, which means it's guaranteed. 9. 2/10 = 1/5 - So the probability of selecting an even number greater than 4 is 1/5 or 20% 14. A) P(not A): P(A)= 69:31 B) P( A ) = 0.31 / 0.69 ≈ 0.449 16. Total outcomes = 82 (against) + 3 (in favor) = 85 P(Fedora wins) = 3 / 85 ≈ 0.0353 21. Fair price = expected value+cost to play Fair price = \$2.50+\$6.50=\$4.00 22. Fair price = \$5.00 - \$1.50 = \$3.50 25. P(even on both wheels) = P(even on outer wheel) * P(even on inner wheel) = (1/4) * (1/4) = 1/16 26. Probability = (Number of sectors greater than 5) / (Total sectors) Probability = 3/8 Joint Probability = (Probability on Wheel 1) * (Probability on Wheel 2) Joint Probability = (3/8) * (3/8) = 9/64