Answer:
15 heads out of 30
Step-by-step explanation:
The total number of possible sequences of coin flips can be determined by raising the number of outcomes, which is 2 for any coin (heads or tails), to the power of the number of times the coin is flipped, given by the question as 30. Therefore, 230 is the total number of different sequences for 30 coin flips.
We can use combinatorial math to find the number of sequences with exactly 15 heads, which is 30 choose 15 or (3015) . The probability we are looking for will be the number of sequences with 15 heads divided by the total possible sequences.
Now we can express the whole probability in math notation, and calculate an answer (rounded to 4 decimal places):
(3015)230=1551175201073741824≈0.1445≈14.45%
15 heads out of 30 is the most likely outcome when flipping 30 coins, if you run the same calculation with 14 or 16 heads you will get two equal, but smaller probabilities, same with 13 and 17 heads, and so on. If you graphed all of the outcomes, you will find it follows a normal distribution, or Bell curve, with the outcome of 15 heads, located at the peak.
