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Two Dice Are Thrown. the Events A, B, C, D, E And F Are Described as :(Ii) State True Or False: - Mathematics

Two dice are thrown. The events ABCDE and F are described as :
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.

State true or false:
(a) A and B are mutually exclusive.
(b) A and B are mutually exclusive and exhaustive events.
(c) A and C are mutually exclusive events.
(d) C and D are mutually exclusive and exhaustive events.
(e) CD and E are mutually exclusive and exhaustive events.
(f) A' and B' are mutually exclusive events.
(g) ABF are mutually exclusive and exhaustive events.

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Solution

When two dices are thrown, there are 62 = 36 possible outcomes.
= Getting an even number on the first dice
    = {(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 = Getting an odd number on the first dice
     = {(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 = Getting at most 5 as the sum of the numbers on the two dices.
    = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2),             (4,1)}
D = Getting a sum greater than 5 but less than 10
    = {(1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6),
         (4, 2), (4, 3), (4, 4), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (6, 1),               (6,2), (6, 3)}
E = Getting at least 10 as the sum of the numbers on the dices
   = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
= Getting an odd number on one of the dices
   = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6),
        (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5)}
Now,

(a) True, because A ∩ B = Φ
(b) True, because A ∩ B = Φ and A ∪ B = S
(c) False, because A ∩ C ≠  Φ
(d) False, because C ∩ D = Φ but C ∪ D ≠ S
(e) True, because C ∩ D ∩ E = Φ and C ∪ D ∪ E = S
(f) True, because A' ∩ B' = Φ
(g) False, because A ∩ B ∩ F ≠ Φ and A ∪ B ∪ F = S

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.2 | Q 7.2 | Page 16
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