A fair coin and a fair die are both tossed and the result is recorded using an o

Question

A fair coin and a fair die are both tossed and the result is recorded using an ordered pair with the coin toss (H or T) first and the die face (1,…,6) second. Please answer the following:

a. Find the sample space S for the experiment:

Let A be the event that the coin toss is a head and B be the event that the die shows an even number. Find each of the following events (i.e. find the set of outcomes that comprises each of these events): (Note A' = complement; B' = complement)

b. A (intersection) B =

c. A' (intersection) B' =

d. A (union) B =

e. A' (union) B' =

Explanation / Answer

a) samle space S ={ H1 ;H2 ; H3 ; H4 ; H5 ; H6 ;T1 ;T2 ; T3 ; T4 ; T5 ; T6 }

b) A n B ={H2 ; H4 ; H6}

c) A' n B' = {T1 ;T3 ;T5}

d) A U B =(H1 ;H2 ; H3 ; H4 ; H5 ; H6 ; T2 ; T4 ; T6 }

e) A 'U B' ={ H1 ; H3 ; H5 ;T1 ;T2 ; T3 ; T4 ; T5 ; T6 }

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