. [15 pts] Consider a random permutation of the decimal digits, that is, of the numbers...

Transcribed Image Text:

. [15 pts] Consider a random permutation of the decimal digits, that is, of the numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the following two events: fro E is "the first digit is 9 or the last digit is 0. F is "the first digit is (9 or 8) and the last digit is 0". (a) [5 pts] Calculate Pr[E]. (b) [5 pts] Calculate Pr[F]. (c) [5 pts] Prove or disprove: ELF. We know this probability space from lecture, no need to describe it. However, justify your answers! Solution. (a) YOUR SOLUTION TO PART (a) HERE (b) YOUR SOLUTION TO PART (b) HERE (c) YOUR SOLUTION TO PART (c) HERE . [15 pts] Consider a random permutation of the decimal digits, that is, of the numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the following two events: fro E is "the first digit is 9 or the last digit is 0. F is "the first digit is (9 or 8) and the last digit is 0". (a) [5 pts] Calculate Pr[E]. (b) [5 pts] Calculate Pr[F]. (c) [5 pts] Prove or disprove: ELF. We know this probability space from lecture, no need to describe it. However, justify your answers! Solution. (a) YOUR SOLUTION TO PART (a) HERE (b) YOUR SOLUTION TO PART (b) HERE (c) YOUR SOLUTION TO PART (c) HERE