Two dice are thrown. The events A, B, and C are as follows. A: getting

1.	Two dice are thrown. The events A, B, and C are as follows. A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the numbers on the dice < 5. Describe the events: (i) A’ (ii) not B (iii) A or B (iv) A and B (v) A but not C (vi) B or C (vii) B and C (viii) A∩B’∩C’.
Answer» We have, sample space S of the experiment is 5 = {(x,y):x,y = l,2,3,4,5,6} Then A = {(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4.1), (4,2), (4,3), (4,4), (4,5), (4,6) (6.1),(6,2),(6,3),(6,4),(6,5),(6,6)} B = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (3.1) , (3,2), (3,3), (3,4), (3,5), (3,6), (5.1) , (5,2), (5,3), (5,4), (5,5), (5,6)} C = {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3) (3.1) , (3,2), (4,1)} (i) A’ = B (ii) B’ = A (iii) A∪B = S (iv) A∩B = ϕ (v) A – C = {(2,4),(2,5),(2,6),(4,2),(4,3) , (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4),(6,5),(6,6)} (vi) B ∪ C = {(1,1), (1,2), ………… (1,6), (2,1), (2,2), (2.3),(3,1), (3,2), (3,3), ……….. (3,6), (4,1), (5,1), (5,2),(5,6)} (vii) B ∩ C = {(1,1),(1,2),(1,3),(1,4),(3,1),(3,2)} (viii) Here, C’ = S – C and B’ = A ∴ A ∩ B’∩ C’ = A ∩ A ∩ C’ = A ∩ C’ = {(2,4), (2,5), (2,6), (4,2), (4.3), (4,4), …………, (4,6), (6,1), (6,2), ………. , (6,6)}

Two dice are thrown. The events A, B, and C are as follows. A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the numbers on the dice < 5. Describe the events: (i) A’ (ii) not B (iii) A or B (iv) A and B (v) A but not C (vi) B or C (vii) B and C (viii) A∩B’∩C’.

Answer»

We have, sample space S of the experiment is 5 = {(x,y):x,y = l,2,3,4,5,6}

Then A = {(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4.1), (4,2), (4,3), (4,4), (4,5), (4,6) (6.1),(6,2),(6,3),(6,4),(6,5),(6,6)}

B = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (3.1) , (3,2), (3,3), (3,4), (3,5), (3,6), (5.1) , (5,2), (5,3), (5,4), (5,5), (5,6)}

C = {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3) (3.1) , (3,2), (4,1)}

(i) A’ = B

(ii) B’ = A

(iii) A∪B = S

(iv) A∩B = ϕ

(v) A – C = {(2,4),(2,5),(2,6),(4,2),(4,3) , (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}

(vi) B ∪ C = {(1,1), (1,2), ………… (1,6), (2,1), (2,2), (2.3),(3,1), (3,2), (3,3), ……….. (3,6), (4,1), (5,1), (5,2),(5,6)}

(vii) B ∩ C = {(1,1),(1,2),(1,3),(1,4),(3,1),(3,2)}

(viii) Here, C’ = S – C and B’ = A

∴ A ∩ B’∩ C’ = A ∩ A ∩ C’

= A ∩ C’

= {(2,4), (2,5), (2,6), (4,2), (4.3), (4,4), …………, (4,6), (6,1), (6,2), ………. , (6,6)}