Question

analyze the table representing five experiments with an increasing number of trials. the table shows the frequency of a coin landing heads up or tails up. what can you predict regarding the probability of the coin landing heads up? options: the frequency does not change with more trials. the experimental probability increases with more trials. with more trials, the frequency of heads up will equal the frequency of tails up. the frequency of heads up decreases with more trials.

Explanation:

1. Calculate the experimental probability (frequency) of heads for each experiment:

• Experiment 1: $\frac{12}{20} = 0.6$
• Experiment 2: $\frac{25}{40} = 0.625$
• Experiment 3: $\frac{20}{60} \approx 0.333$ (This seems inconsistent, maybe a typo? If we assume it's 30 instead of 20, $\frac{30}{60}=0.5$; if 25, $\frac{25}{60}\approx0.417$)
• Experiment 4: $\frac{35}{80} = 0.4375$
• Experiment 5: $\frac{48}{100} = 0.48$

1. As the number of trials increases, the law of large numbers states that the experimental probability (frequency) of an event (like heads in a fair coin toss) approaches the theoretical probability (0.5 for a fair coin, meaning heads and tails frequencies should become equal with a large number of trials). The other options are incorrect:

• "The frequency does not change with more trials" is wrong as seen from the changing frequencies.
• "The experimental probability increases with more trials" is wrong as the frequencies don't show a consistent increase.
• "The frequency of heads up decreases with more trials" is wrong as the frequencies don't show a consistent decrease.
• The correct reasoning is based on the law of large numbers, which implies that with more trials, the frequency of heads (and tails) should approach equality for a fair coin.

Answer:

With more trials, the frequency of heads up will equal the frequency of tails up.