1 Suppose that a coin is flipped and a die is rolled Let E1

1) Suppose that a coin is flipped and a die is rolled. Let E1 denote the event “the coin shows a tail”, let E2 denote the event “the die shows a 3”, let E3 denote the event “the coin shows heads and the die shows an odd number”.

        a) List the element of the event E1 or E2.

        b) Are E1 and E3 mutually exclusive?

2) Determine how many strings can be formed by ordering the letters ABCDE :
        a) Contains the substring ACE
        b) Contains either the substring AE or the substring EA or both.

Solution

a) E1 or E2 = (T1, T2, T3,T4,T5,T6, H3, T3}

b) E3 = coin shows head or die shows odd number

E3 = (H1, H2, H3, H4, H5,H6,T1,T3,T5}

E1 and E3 donot have common so mutually exclusive.

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