Question

which table represents the sample space of this compound event? heads (h) tails (t) heads (h) hh ht tails (t) th tt heads (h) tails (t) heads (h) ht tt tails (t) tt tt heads (h) tails (t) heads (h) hh ht heads (h) hh ht heads (h) heads (h) heads (h) hh hh tails (t) th th

Explanation:

Step1: Analyze coin - toss sample space

When tossing a coin twice, the first - toss has 2 outcomes (heads or tails) and for each outcome of the first toss, the second toss also has 2 outcomes.
The sample space consists of all possible pairs of outcomes. The possible pairs are (heads, heads) written as HH, (heads, tails) written as HT, (tails, heads) written as TH, and (tails, tails) written as TT.

Step2: Match with given tables

The first table has the correct combinations of HH, HT, TH, and TT. The second table has incorrect combinations (e.g., multiple TT in wrong places). The third table has repeated first - toss values instead of considering two different tosses properly. The fourth table has incorrect combinations as well.

Answer:

The first table (with heads (H) and tails (T) in the first row and first column and HH, HT, TH, TT in the cells) represents the sample space of the compound event.