Question

question 7 (multiple choice worth 2 points) (events and sample spaces lc) list all the possible outcomes from flipping a coin twice and rolling a four - sided die. {h1, h2, h3, h4, t1, t2, t3, t4} {hh1, hh2, hh3, hh4, hh5, hh6, ht1, ht2, ht3, ht4, th1, th2, th3, th4, tt1, tt2, tt3, tt4} {hh1, hh2, hh3, hh4, ht1, ht2, ht3, ht4, th1, th2, th3, th4} {hh1, hh2, hh3, hh4, ht1, ht2, ht3, ht4, th1, th2, th3, th4, tt1, tt2, tt3, tt4}

Explanation:

Step1: Analyze coin - flip outcomes

When flipping a coin twice, there are 4 possible coin - flip combinations: HH, HT, TH, TT.

Step2: Analyze die - roll outcomes

When rolling a four - sided die, there are 4 possible outcomes: 1, 2, 3, 4.

Step3: Combine outcomes

By the multiplication principle, for each coin - flip combination, there are 4 die - roll outcomes. So the total number of combined outcomes is \(4\times4 = 16\). The sample space is \(\{HH1, HH2, HH3, HH4, HT1, HT2, HT3, HT4, TH1, TH2, TH3, TH4, TT1, TT2, TT3, TT4\}\)

Answer:

\(\{HH1, HH2, HH3, HH4, HT1, HT2, HT3, HT4, TH1, TH2, TH3, TH4, TT1, TT2, TT3, TT4\}\)