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Fudgin [204]
2 years ago
10

We choose a number from the set 1, 2, 3,..., 100 uniformly at random and denote this number by X. For each of the following choi

ces decide whether the two events in question are independent or not.
a. A = {X is even), B-(X is divisible by 5}
b. C= (X has two digits), D = {X is divisible by 31}
c. E= {X is a prime), F = {X has a digit 5}
Mathematics
1 answer:
kiruha [24]2 years ago
5 0

Answer:

(a) A and B are dependent.

(b) C and D are dependent.

(c) E and F are dependent.

Step-by-step explanation:

Two sets are said to be independent if the intersection of the two set is empty. That is the sets are disjoint.

Let's examine the situations to determine if they are independent or not.

(a) A = {2, 4, 6, . . . , 10, . . . , 20, . . .} and B = {5, 10, 15, . . . , 20, . . .}. Since A n B = {10, 20, . . .}, then the sets are dependent

(b) C = {10, 11, 12, . . . , 31, . . . , 62, . . . , 93, . . .} and D = {31, 62, 93}. Since C n D = {31, 62, 93}, then the sets are dependent.

(c) E = {5, 7, 11, . . .} and F = {5, 15, . . .}. Since E n F = {5}, then the set are dependent.

Thus

(a) A and B are dependent.

(b) C and D are dependent.

(c) E and F are dependent.

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