University:
Boston University
Course:
CGS MA 121 | Calculus
Academic year:

2024
Views:

115

Pages:

3
Author:

fiziokrat16l

Question 1 What is the mean, median, mode, and range of the following numbers?: {1, 2, 3, 4, 5, 6, 7,8,9} Answer Mean = 5 and Median = 5 There is no mode Range = 9 - 1 = 8 Solution: We have the distribution: 1, 2, 3, 4, 5, 6, 7, 8, 9 The Range is the difference between the highest and the lowest - an indication of how far the numbers are spread out. range = 9 - 1 = 8 Mode, median and mean are all regarded as different types of average, they give different information. The Mode is the value with the highest frequency - the one that occurs the most often. There is no mode in this case because each number occurs exactly once. The median is the number exactly in the middle of a set of numbers arranged in order. There are 9 numbers, the middle one is 5 There are 4 numbers on each side. 1, 2, 3, 4, 5, 6, 7, 8, 9 The mean is what is generally understood as average Mean = sum of the values / the number of values Mean = (1+2+3+4+5+6+7+8+9) / 9 = 45/9 = 5 Question 2 How do you calculate expected value? Answer Same thing as the mean Explanation: Expected value is another way of stating the mean. It can be calculated one of two ways: For a set of numbers, take the sum divided by the number of data points. So 4,6,11: (4 + 6 + 11) / 3 = 21 / 3 = 7 Question 3 If you flip a coin three times, what is the probability of getting tails three times? Answer To calculate the probability you have to name all possible results first. If you mark a result of a single coin flip as H for heads or T for tails all results of 3 flips can be written as: Ω = {(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)} Each triplet contains results on 1st, 2nd and 3rd coin. So you can see that in total there are 8 elementary events in Ω. |Ω| = 8 Now we have to define event A of getting tails three times. The only elementary event which satisfies this condition is (T, T, T) so we can write that: A = {(T,T,T)} |A| = 1 Now according to the (classic) definition of probability we can write, that: P(A) = |A| / |Ω| = 1 / 8 So finally we can write the answer: Probability of getting 3 tails in 3 coin flips is 1/8 Question 4 If you flip a coin and roll a die, what is the probability that you will flip a heads and roll a 3? Answer When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes (1 to 6). Putting these together means you have a total of 2 x 6 = 12 outcomes. P(H,3) = P(H) × P(3) = 1/2 * 1/6 = 1/12 The chances of flipping a head and rolling a 3 is 1/12 Question 5 The probability of drawing a green candy from a jar of 20 candies is 1/4. How many yellow candies should be added to the jar in order to reduce the probability to 1/6 ? Answer The probability of drawing a green candy from a jar of 20 candies = 1/4 number of green candies in the jar = 20 * (1/4) = 5. We add x yellow candies. Total number of candies become 20 + x and probability of drawing a green candy from a jar becomes 5 / (20 + x) As we desire the probability to be 1/6, we have: 5 / (20 + x) = 1/6 or (20+x) = 5 * 6 = 30 and x = 30 - 20 = 10 So, 10 yellow candies should be added to the jar in order to reduce the probability to 1/6. 32.0s