Answer to Question #144819 in Statistics and Probability for Cameron Foster

Question

1. Serah needs access to Academia’s historical records. She must input a 5 digit code to access the
computer. Please find the following. Keep you solutions exact to four decimal places if needed.
(a) Calculate the Sample Space
(b) What is the probability the code contains no repeats?
(c) What is the probability the code ends with an even number?
(d) What is the probability the code contains only odd numbers?
(e) What is the probability the code ends with 2?

Answer 1

a. We can choose every digit from 0,1,2,3,4,5,6,7,8,9. So we have 10 options ( n1=10, n2=10, n3=10, n4=10, n5=10).

Sample Space N=n1xn2xn3xn4xn5=10⁵

b. To choose first digit we have 10 options, second digit - 9 options, third - 8 options, fourth - 7 options, five's - 6 options. So code with no repeats can be obtained in N1= 10x9x8x7x6= 30240 options. Probability that the code contains no repeats is N1/N =30240/10⁵ =0.3024

c. Even digits are 0,2,4,6,8. So we have 5 options of the last digit. So code ends with an even number can be obtained in N2=5x10⁴ =50000 options. Probability that the code ends with an even number is P=N2/N=5x10⁴ /10⁵ =0.5000

d. Odd numbers are 1,3,5,7,9. So we have 5 options for choosing each digit. So code containing only odd numbers can be obtained in N3=5⁵=3125 options. Probability that the code contains only odd numbers is P=N3/N=3125/10⁵ =0.0313

e. We have only one option for the last digit is 2. So code ends with 2 can be obtained in N4=1x10⁴ options. Probability that the code ends with 2 is P=N4/N=10⁴/10⁵=0.1000.