Step-by-step explanation:

Given:

Sample Space = (0,1,2,3,4,5,6,7,8,9)

A = (0,1,2,3,4)

B = (0,2,4,6,8)

C = (1,3,5,7,9)

We can use the following formulas to find the probabilities:

1. P(A ∩ B) represents the probability of the intersection of A and B.

P(A ∩ B) = |A ∩ B| / |Sample Space|

|A ∩ B| represents the number of elements that are common to both A and B.

|A ∩ B| = |{0, 2, 4}| = 3

|Sample Space| = 10

P(A ∩ B) = 3/10 = 0.3

2. P(A ∩ C) represents the probability of the intersection of A and C.

P(A ∩ C) = |A ∩ C| / |Sample Space|

|A ∩ C| represents the number of elements that are common to both A and C.

|A ∩ C| = |{1, 3}| = 2

|Sample Space| = 10

P(A ∩ C) = 2/10 = 0.2

3. P(A) represents the probability of A.

P(A) = |A| / |Sample Space|

|A| represents the number of elements in A.

|A| = 5

|Sample Space| = 10

P(A) = 5/10 = 0.5

4. P(B) represents the probability of B.

P(B) = |B| / |Sample Space|

|B| represents the number of elements in B.

|B| = 5

|Sample Space| = 10

P(B) = 5/10 = 0.5

5. P(C) represents the probability of C.

P(C) = |C| / |Sample Space|

|C| represents the number of elements in C.

|C| = 5

|Sample Space| = 10

P(C) = 5/10 = 0.5

Therefore, the answers are:

1. P(A ∩ B) = 0.3

2. P(A ∩ C) = 0.2

3. P(A) = 0.5

4. P(B) = 0.5

5. P(C) = 0.5