G163 STA1625_MODULE03_PROBABILITY OF EVENTS_01.21.24

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Rasmussen College, Florida *

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Statistics

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May 29, 2024

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Module 03: Probability of Events Rasmussen University G163/STA1625 Essential Statistics and Analytics

PART 01- DATA TABLE AVERAGE NUMBER OF HOURS SLEEP PER NIGHT  6 HOURS  6 HOURS TOTAL STUDENT 1 5 6 NOT A STUDENT 3 1 4 TOTAL 4 6 10 PART 02- PROBABILITY QUESTIONS 1. What is the probability that a randomly selected person slept less than an average of 6 hours per night?  The probability would be 0.4 – Given that 4 out of the 10 individuals slept less than 6 hours.  The equation would be P(<6)= 4  10 = 0.4 2. What is the probability that a randomly selected person is a student?  The probability would be 0.6 – Given that out of the 10 individuals 6 of them were students.  The equation would be P(S)= 6  10 = 0.6 3. What is the probability that a randomly selected student slept greater than an average of 6 hours a night?  The probability would be 0.83 – Given that 5 out of the 6 individuals that slept greater than 6 hours were students.  The equation would be P(>6)= 5  6 = 0.83 4. What is the probability that a randomly selected person who sleeps greater than an average of 6 hours a night is not a student?  The probability would be 0.17- Given than out of the 6 individuals who slept more than 6 hours only 1 was not a student.  The equation would be P(NS | >6)= 1  6 = 0.17 5. What is the probability that a randomly selected person is not a student or slept less than an average of 6 hours a night?  The probability would be 0.75- Given that there were a total of 4 individuals who slept less than 6 hours and 3 of them were not students.  The equation would be P(NS |<6)= 3  4 = 0.75

PART 03- COUNTING QUESTIONS 1. You’d like to gain more information from a subset of people you know. You want to choose 5 people from your group of 10 that you surveyed to ask additional questions. How many ways can you pick this subset of 5 people?  Using the formula for Combination there would be a total of 252 ways. o nCx= n!  r!(n-r)! n=10 r=5 o 10C5 =10!  5!(10-5)! o 10C5= 10!  5!(5)! o 10C5 = 10×9×8×7×6×5×4×3×2×1  (5x4x3x2x1) (5x4x3x2x1) o 10C5 = 3,628,800  120x120 o 10C5 = 3,628,800  14,400 o 10C5= 252 2. You are thanking the people for participating in your survey. You have three gift cards: $50 Target gift card, $25 Amazon gift card, and $10 Starbucks gift card. You place all 10 names in a hat and randomly select who will get each gift card. Note: only one person can get a gift card, and no one can get more than one gift card. In how many ways can you give out the gift cards?  Using the permutation formula there would be 720 ways o 10p3 o 10p3= 10!  (10-3)! = 10x9x8 o =720

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G163 STA1625_MODULE03_PROBABILITY OF EVENTS_01.21.24

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