Question 974418
Here are my results when I flipped 2 coins 50 times (H = heads, T = tails)


Each pair of flips represents a single independent trial. Instead of making one long 50x2 table, I made the table a bit more compact (5 columns, 10 trials per column)


<table border=1><tr><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th></tr><tr><td>1</td><td>HH</td><td>11</td><td>TT</td><td>21</td><td>TT</td><td>31</td><td>TH</td><td>41</td><td>TT</td></tr><tr><td>2</td><td>TT</td><td>12</td><td>HH</td><td>22</td><td>HH</td><td>32</td><td>HH</td><td>42</td><td>TT</td></tr><tr><td>3</td><td>HT</td><td>13</td><td>HH</td><td>23</td><td>TH</td><td>33</td><td>HT</td><td>43</td><td>TT</td></tr><tr><td>4</td><td>TH</td><td>14</td><td>TH</td><td>24</td><td>TT</td><td>34</td><td>TH</td><td>44</td><td>HT</td></tr><tr><td>5</td><td>TT</td><td>15</td><td>TH</td><td>25</td><td>HT</td><td>35</td><td>HH</td><td>45</td><td>HH</td></tr><tr><td>6</td><td>TH</td><td>16</td><td>TH</td><td>26</td><td>TH</td><td>36</td><td>HH</td><td>46</td><td>TT</td></tr><tr><td>7</td><td>TT</td><td>17</td><td>HT</td><td>27</td><td>TT</td><td>37</td><td>TT</td><td>47</td><td>TT</td></tr><tr><td>8</td><td>HH</td><td>18</td><td>HH</td><td>28</td><td>TH</td><td>38</td><td>HH</td><td>48</td><td>HH</td></tr><tr><td>9</td><td>HH</td><td>19</td><td>HT</td><td>29</td><td>HH</td><td>39</td><td>TT</td><td>49</td><td>TH</td></tr><tr><td>10</td><td>TH</td><td>20</td><td>TT</td><td>30</td><td>TH</td><td>40</td><td>TH</td><td>50</td><td>HT</td></tr></table>


In <font color="red">red</font> are the trials where exactly one head pops up (either HT or TH)


<table border=1><tr><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th><th>Trial</th><th>Result</th></tr><tr><td>1</td><td>HH</td><td>11</td><td>TT</td><td>21</td><td>TT</td><td>31</td><td><font color="red">TH</font></td><td>41</td><td>TT</td></tr><tr><td>2</td><td>TT</td><td>12</td><td>HH</td><td>22</td><td>HH</td><td>32</td><td>HH</td><td>42</td><td>TT</td></tr><tr><td>3</td><td><font color="red">HT</font></td><td>13</td><td>HH</td><td>23</td><td><font color="red">TH</font></td><td>33</td><td><font color="red">HT</font></td><td>43</td><td>TT</td></tr><tr><td>4</td><td><font color="red">TH</font></td><td>14</td><td><font color="red">TH</font></td><td>24</td><td>TT</td><td>34</td><td><font color="red">TH</font></td><td>44</td><td><font color="red">HT</font></td></tr><tr><td>5</td><td>TT</td><td>15</td><td><font color="red">TH</font></td><td>25</td><td><font color="red">HT</font></td><td>35</td><td>HH</td><td>45</td><td>HH</td></tr><tr><td>6</td><td><font color="red">TH</font></td><td>16</td><td><font color="red">TH</font></td><td>26</td><td><font color="red">TH</font></td><td>36</td><td>HH</td><td>46</td><td>TT</td></tr><tr><td>7</td><td>TT</td><td>17</td><td><font color="red">HT</font></td><td>27</td><td>TT</td><td>37</td><td>TT</td><td>47</td><td>TT</td></tr><tr><td>8</td><td>HH</td><td>18</td><td>HH</td><td>28</td><td><font color="red">TH</font></td><td>38</td><td>HH</td><td>48</td><td>HH</td></tr><tr><td>9</td><td>HH</td><td>19</td><td><font color="red">HT</font></td><td>29</td><td>HH</td><td>39</td><td>TT</td><td>49</td><td><font color="red">TH</font></td></tr><tr><td>10</td><td><font color="red">TH</font></td><td>20</td><td>TT</td><td>30</td><td><font color="red">TH</font></td><td>40</td><td><font color="red">TH</font></td><td>50</td><td><font color="red">HT</font></td></tr></table>


There are 21 trials with a red HT or TH in them. The rest are either HH or TT.


There are 50 trials total. So the empirical probability is 21/50 = 0.42 which is pretty close to the theoretical probability of 1/2 = 0.5


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