Question

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 1

Given:

Two dice are thrown.

Events are defined as:

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 two dice ≤ 5

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(i) A′ (Not A)

Getting an odd number on the first die.

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(ii) Not B (B′)

Getting an even number on the first die.

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(iii) A or B (A ∪ B)

Getting either an even or an odd number on the first die.

(This is a certain event, since every number on a die is either even or odd.)

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(iv) A and B (A ∩ B)

Getting a number on the first die which is both even and odd.

(This is an impossible event.)

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(v) A but not C (A ∩ C′)

Getting an even number on the first die and
the sum of the two dice is greater than 5.

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(vi) B or C (B ∪ C)

Getting an odd number on the first die or
the sum of the numbers on the two dice is ≤ 5.

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(vii) B and C (B ∩ C)

Getting an odd number on the first die and
the sum of the numbers on the two dice is ≤ 5.

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(viii) A ∩ B′ ∩ C′

Getting an even number on the first die,
not getting an odd number on the first die (i.e., still even), and
the sum of the numbers on the two dice is greater than 5.

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Summary:

These statements describe combinations of conditions involving the parity of the first die and the sum of both dice.