A die is rolled e is the event that the uppermost face shows a prime number what is e equal to

Sample Space = {1, 2, 3, 4, 5, 6}∴ n(S) = 6 A = {2, 4, 6}∴ n(A) = 3,B = {1, 3, 5}∴ n(B) = 3,C = {2, 3, 5}

∴ n(C) = 3

Page 2

Sample Space (S) = `{[(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)],[(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)], [(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)],[(4,1) (4,2)(4,3)(4,4)(4,5)(4,6)],[(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)],[(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)]}`

∴ n(S) = 36A = {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (6, 6)}

∴ n(A) = 6

B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)}∴ n(B) = 6C = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}

∴ n(C) = 6

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Sample Space (S) = {HHH, HHT, HTT, HTH, THT, TTH, THH, TTT}∴ n(S) = 8 A = {HHH, HHT, HTH, THH}∴ n(A) = 4 B = {TTT}∴ n(B) = 1 C = {HHH, HHT, THT ,THH}

∴ n(C) = 4

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A die is rolled and the number showing is observed. Determine whether the events $E$ and $F$ are mutually exclusive. Then find the probability of the event $E \cup F .$ (a) $E :$ The number is greater than 3 $F :$ The number is less than 5 (b) $E :$ The number is divisible by 3 $F :$ The number is less than 3