Question

A coin is tossed twice. Let S be the set of all possible pairs that can be observed, i.e., S = {H, T} x {H, T} = {(H, H), (H, T), (T, H), (T, T)}. Write the following sets by listing their elements: A: the first coin toss results in a head. B: At least one tail is observed. C: The two coin tosses result in different outcomes.

Answer 1

Set Elements:

(a) A: The first coin toss results in a head.

Elements: {(H,H), (H,T)}

(b) B: At least one tail is observed.

Elements: {(H,T), (T,H), (T,T)}

(c) C: The two coin tosses result in different outcomes.

Elements: {(H,T), (T,H), (T,T)}

(a): We only need to consider the first outcome of each pair in the set S. If the first outcome is H, then the elements are (H,H) and (H,T).

(b): Any pair with at least one T will be included. This eliminates (H,H) and leaves {(H,T), (T,H), (T,T)}.

(c): The two outcomes need to be different for each pair. This removes (H,H) and (T,T), leaving {(H,T), (T,H)}.