Six digits are chosen randomly from the set {0,1,2,…,9} a.) What is the probability that all six digits are the same? b.) What is the probability that five or more of the digits of the same?

Answer:a) 0.00001b) 0.001Step-by-step explanation:Given numbers,0, 1, 2, 3, 4, 5, 6, 7, 8, 9a) If by these numbers we have to make six digit number,So, the total ways of arranging 6 digit number = [tex]10^6[/tex]Now, if all six digit in the number are same,Then the possible ways = 10   ( eg : 000000, 111111, 222222, 333333, 444444... etc ),Hence, the probability that all six digits are the same [tex]=\frac{10}{10^6}=\frac{1}{10^5}=0.00001[/tex]b) The ways that five or more of the digits of the same = exactly 5 digits are same + Exactly 6 digits are same∵ The ways that 5 digits are same = 10 × 9 = 90 (i.e. 111110, 111112, 111113,.....9 times, 222220, 222221,.....9 times .... etc..)So, the number of ways that 5 or more than 5 digits are same = 90 + 10 = 100Hence, the probability that five or more of the digits of the same [tex]=\frac{100}{10^5}[/tex][tex]=0.001[/tex]