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Theoretical Probabilities of Coin Tosses (Part 2) hink of tossing a coin 10 times as a binomial probability experiment, where the probability of heads is p = 0.5. Compute the remaining theoretical probabilities of obtaining a certain number of heads in 10 tosses in the table elow* Enter the results from your empirical trials in the last two columns. (Ex: the empirical probability of obtaining exactly 4 heads in 10 tosses is the proportion of your twelve trials that resulted in obtaining 4 heads.) No. of heads 0 1 2 3 4 No. of combinations 10! 0! (10-0)! 10! 1! (10-1)! 10! 2! (10-2)! G 10! 3! (10-3)! = 1 =10 = 45 = 120 10! 3! (10-3)! = 120 Probability of an individual outcome 1 2 1 2 1 2 HIN 1 10 ¹× (-)* ×(₁-)" = 1 x 1- Theoretical Probability 45 1 10 × () ×(1--) = 120 1- = 0.001 8 = 0.01 = 0.044 = 0.117 Frequency of trials with this No. of heads Empirical Probability of this No. of heads

Theoretical Probabilities of Coin Tosses (Part 2) hink of tossing a coin 10 times as a binomial probability experiment, where the probability of heads is p = 0.5. Compute the remaining theoretical probabilities of obtaining a certain number of heads in 10 tosses in the table elow* Enter the results from your empirical trials in the last two columns. (Ex: the empirical probability of obtaining exactly 4 heads in 10 tosses is the proportion of your twelve trials that resulted in obtaining 4 heads.) No. of heads 0 1 2 3 4 No. of combinations 10! 0! (10-0)! 10! 1! (10-1)! 10! 2! (10-2)! G 10! 3! (10-3)! = 1 =10 = 45 = 120 10! 3! (10-3)! = 120 Probability of an individual outcome 1 2 1 2 1 2 HIN 1 10 ¹× (-)* ×(₁-)" = 1 x 1- Theoretical Probability 45 1 10 × () ×(1--) = 120 1- = 0.001 8 = 0.01 = 0.044 = 0.117 Frequency of trials with this No. of heads Empirical Probability of this No. of heads

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Theoretical Probabilities of Coin Tosses (Part 2) Think of tossing a coin 10 times as a binomial probability experiment, where the probability of heads is p = 0.5. Compute the remaining theoretical probabilities of obtaining a certain number of heads in 10 tosses in the table below* Enter the results from your empirical trials in the last two columns. (Ex: the empirical probability of obtaining exactly 4 heads in 10 tosses is the proportion of your twelve trials that resulted in obtaining 4 heads.) + No. of heads 0 2 3 5 6 7 8 9 10 No. of combinations 10! 0! (10-0) 10! 1! (10-1)! <<= 10 10! 2: (10-2)! = 1 10! 3! (10-3)! = 45 <= 120 10! 3! (10-3)! <= 120 Probability of an individual outcome 13 1 2 HİN 2 12 IN 15 13 2 10 x Theoretical Probability × (²) ×(1-1) = 0. 120 10 8 = 0.001 2 45 ()*(1-3)* -0.044 7 0.01 = 0.117 Frequency of trials with this No. of heads Empirical Probability of this No. of heads
Transcribed Image Text:Theoretical Probabilities of Coin Tosses (Part 2) Think of tossing a coin 10 times as a binomial probability experiment, where the probability of heads is p = 0.5. Compute the remaining theoretical probabilities of obtaining a certain number of heads in 10 tosses in the table below* Enter the results from your empirical trials in the last two columns. (Ex: the empirical probability of obtaining exactly 4 heads in 10 tosses is the proportion of your twelve trials that resulted in obtaining 4 heads.) + No. of heads 0 2 3 5 6 7 8 9 10 No. of combinations 10! 0! (10-0) 10! 1! (10-1)! <<= 10 10! 2: (10-2)! = 1 10! 3! (10-3)! = 45 <= 120 10! 3! (10-3)! <= 120 Probability of an individual outcome 13 1 2 HİN 2 12 IN 15 13 2 10 x Theoretical Probability × (²) ×(1-1) = 0. 120 10 8 = 0.001 2 45 ()*(1-3)* -0.044 7 0.01 = 0.117 Frequency of trials with this No. of heads Empirical Probability of this No. of heads
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