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.

(a) write out the sample space ( s ), choosing an ( s ) with equally likely outcomes, if possible. then give the value of ( n(s) ) and tell whether the outcomes in ( s ) are equally likely. let ( h ) represent a heads flip and let ( t ) represent a tails flip. choose the correct answer below.

( \bigcirc ) a. ( s = {hhh, ttt} )

( \bigcirc ) b. ( s = {hh, hth, thh, htt, tht, tth, ttt} )

( \bigcirc ) c. ( s = {hhh} )

( \bigcirc ) d. ( s = {hhhh, hhht, hhth, hthh, thhh, hhtt, hhht, thht, thth, tthh, htth} )

( n(s) = square )

(type a whole number.)

Explanation:

Step1: Identify the sample space

The correct sample space \( S \) is given as \( S = \{hh, hth, thh, htt, tht, tth, ttt\} \) (from option B).

Step2: Count the number of elements

To find \( n(S) \), we count the number of outcomes in the set \( S \). Let's list them: \( hh \), \( hth \), \( thh \), \( htt \), \( tht \), \( tth \), \( ttt \). Counting these, we get 7 elements.

Answer:

\( n(S) = 7 \)