experiment - probability

Question

 An experiment consists of tossing a (fair) coin three times and observing the resulting sequence of heads and tails.  Let E be the event consisting of all outcomes with exactly two heads.

 (a) List all elements in the Sample Space of this experiment

 (b) List all elements in the event E.

 (c) What is the probability of E? (Show all Work)

Answer 1

(a)  The sample space consists of all possible outcomes of the experiment.  Letting h and t stand for heads and tails respectively, and listing the results of a coin toss in the order in which they occur, we have the following possible events:

 

0 heads:

ttt

 

1 head:

tth

tht

htt

 

2 heads:

thh

hth

hht

 

3 heads:

hhh

 

(b)  The elements in the event E (2 heads) are

thh

hth

hht

 

(c)  There are 3 outcomes in the event E, and 8 possible experimental outcomes.

Since each outcome is equally likely, the probability is found as

 

(Number of outcomes in event E) / (Number of possible experimental outcomes)

= 3/8.