Question

a coin is flipped until two heads appear, up to a maximum of three flips. (if two tails are flipped, the coin is still tossed a third time to complete the experiment.) complete parts (a) through (d) below.

(c) write the following event in set notation.
exactly two heads are tossed.
choose the correct answer below.
a. {hh, hth, thh}
b. {hht, htht, thh}
c. {hh}
d. {hh, hth, thh, htth, thth, tthh}

(d) write the following event in set notation.
no heads are tossed.
{ }
(use a comma to separate answers as needed.)

Explanation:

Part (c)

To determine the set for "Exactly two heads are tossed" when flipping a coin until two heads or up to three flips:

• "hh": Two heads in two flips (experiment stops).
• "hth": First head, tail, second head (three flips, two heads).
• "thh": Tail, first head, second head (three flips, two heads).

Option A includes these outcomes. Option B has "hht" (which has two heads but the experiment would stop at "hh" for two heads, so "hht" isn't valid here), "htht" (more than three flips, invalid), so B is wrong. Option C only has "hh", missing the three - flip cases. Option D has extra outcomes with more than two heads or invalid lengths.

The event "No heads are tossed" means all flips are tails. Since we flip up to three times (and even if two tails first, we flip a third time), the only outcome with no heads is three tails, i.e., "ttt".

Answer:

A. {hh, hth, thh}

Part (d)