Let U~ Unif({1,..., 100}), meaning U is chosen uniformly at random from {1,...,100}. Decide whether the...

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Let U~ Unif({1,..., 100}), meaning U is chosen uniformly at random from {1,...,100}. Decide whether the following events are independent: (a) E = {U is even} and F = {U is divisible by 5}. (b) A = {U is prime} and B = {at least one of the digits of U is a 2}. The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. (c) Can you replace the number 100 by a different number, in such a way that your answer to part (a) would change (e.g. if they were indepen- dent before, now they will be dependent)? Let U~ Unif({1,..., 100}), meaning U is chosen uniformly at random from {1,...,100}. Decide whether the following events are independent: (a) E = {U is even} and F = {U is divisible by 5}. (b) A = {U is prime} and B = {at least one of the digits of U is a 2}. The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. (c) Can you replace the number 100 by a different number, in such a way that your answer to part (a) would change (e.g. if they were indepen- dent before, now they will be dependent)?

Answer rating: 100% (QA)

a We can find PE and PF as follows PE the probability that U is even 12 since there are 5 even numbe... View the full answer