Question

A teacher designed a probability simulation using a coin to model the answers of students who guess every answer on a 5-question true- false quiz. In this simulation, a coin is tossed 50 times, and its landing position is recorded. A coin that lands on heads is recorded as a correct answer, while a coin that lands on tail is recorded as an incorrect answer. The results are shown below.

HTHHTHTHTTTTTHHHHTHTHTHTH
HTHHTHTHHTHTTTHTHTTHTHTTT

Which conclusion can be inferred from these results?

The initial coin toss was marked correct 7 times, so a student is likely to get correct answers by guessing.

There was a total of 26 coin tosses that were marked incorrect, so a student will never pass by guessing.

There was no trial in which all 50 coin tosses were marked correct, so a student is more likely to get all incorrect answers by guessing.

There were approximately an equal number of heads and tails in each trial, so the average grade of all students who guess at every item will be about 50%.

Answer 1

The results of the coin toss simulation suggest that the average grade for students guessing on a true-false quiz would be about 50%, as it reflects the approximate equal number of heads and tails, consistent with the law of large numbers in probability.

Step-by-step explanation:

From the probability simulation results provided, where a coin tossed 50 times models the true-false quiz answers, we can infer that there were approximately an equal number of heads and tails. This observation aligns with the fundamental principle of probability which states that if you flip a fair coin, the theoretical probability of getting heads or tails is 0.5. The experiment illustrates the law of large numbers, asserting that as the number of trials increases, the observed relative frequency of occurrences (heads or tails in this case) tends to converge towards the theoretical probability.

Thus, a conclusion that can be inferred from these results is that there were approximately an equal number of heads and tails, which suggests that the average grade of all students who guess on every item of a true-false quiz will be about 50%. This conclusion is based on the premise that each question has an equal chance of being guessed correctly or incorrectly, much like the 50-50 chance of a coin landing on heads or tails.

Answer 2

1. The student got the right answer 24 times out of 50, so 24/50 which is 48/100, so 48%.

2. 48% is approximately 50%, and the number of trials is large enough to infer, by experiment, that 50% of the time the student gets the right answer.

The correct statement is D:
There were approximately an equal number of heads and tails in each trial, so the average grade of all students who guess at every item will be about 50%.

a) 7 is a small number to derive information.
b) In a repetition of the experiment there is a good chance of getting a larger number of H, for example 52% of the time.
c) the probability of getting all answers correct by guessing is
`(1)/(2.2.2........2)= (1)/( 2^(50) )` which is 0 chance.