Question

four students are determining the probability of flipping a coin and it landing heads up. each flips a coin the number of times shown in the table below.

student	number of flips
brady	10
collen	80
deshawn	20

which student is most likely to find that the actual number of times his or her coin lands heads up most closely matches the predicted number of heads - up landings?

Explanation:

Step1: Recall the Law of Large Numbers

The Law of Large Numbers states that as the number of trials (coin flips, in this case) increases, the experimental probability (number of heads divided by number of flips) gets closer to the theoretical probability (for a fair coin, the probability of heads is \( \frac{1}{2} \)). So, the more flips a student does, the more likely the actual number of heads will be close to the predicted number (which is \( \text{number of flips} \times \frac{1}{2} \)).

Step2: Compare the number of flips for each student

• Ana: 50 flips
• Brady: 10 flips
• Collen: 80 flips
• Deshawn: 20 flips

Among these, Collen has the highest number of flips (80). By the Law of Large Numbers, a larger number of trials gives a better approximation of the theoretical probability, so the actual number of heads for Collen is most likely to be close to the predicted number (\( 80 \times \frac{1}{2} = 40 \) heads, but the key here is the number of flips—more flips mean the actual count is more likely to match the predicted count due to the Law of Large Numbers).

Answer:

Collen