STA 1053-Homework #3 Due Date: February 19, 2018 3 1. Assume that you have a fai
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Question
STA 1053-Homework #3 Due Date: February 19, 2018 3 1. Assume that you have a fair die with faces numbered 1 through 6. You roll the die three times What is the probability that... (a) .. . you o a odd numbers? (b) ..you roll at least one even number? (c)..you roll a 3 or greater on all three rolls? (d three of the rolls are different? 2. You never know when you're going to need change, which is why Prof. Panda always carries exactly 99 cents in his pocket at all times: 3 quarters (25 cents each), 1 dime (10 cents), 2 nickels (5 cents each), and 4 pennies (1 cent each). Suppose that he randomly draws three coins, one at a time and without replacement, from his pocket. What is the probability that... (a) ..exactly two of the three coins drawn are quarters? (b).. he draws exactly one penny, one nickel, and one quarter? (c) ..the first coin drawn is the dime, and that the second and third coins drawn are both worth less than the dime? (d) ..one of the coins drawn is the dime? 3. A test used on a computer's motherboards correctly indicates the presence of a particular defect 96.7% of the time when the motherboard actually is defective. The test also correctly indicates that there is no defect 98.3% of the time when the motherboard is actually not defective. Suppose, from previous experience, we know that only 0.3% of motherboards actually have this defect. What is the probability that the motherboard actually is defective, given that the test indicates it is defective?
Explanation / Answer
1. total number of outcomes = 6^3
a. P(all odd numbers) = P( 1 0r 3 0r 5)= (3/6)^3 = (1/2)^3 = 1/8
b. P,[ at least one even number ] = 1 - P [ all odd numbers ] = 1- (1/8) = 7/8
c. P[ you roll a 3 or more on all three rolls ] = (4/6)^3 = 0.2962963
d. P [ all three of them are different ] = 3! * (1/6)* (1/5) *(1/4) = 0.008333333*6 = 0.5
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