Question

A class quiz has 5 True/False questions. The correct answers are T, T, F, F, and T, in that order. John answered the questions randomly and is now wondering if he will pass the quiz. He needs to have at least 3 correct answers. John used a calculator to generate random numbers from 1 to 100. He let odd numbers stand for True and even numbers stand for False. He recorded the results in the table. What is the experimental probability that John passed the quiz?.

Answer 1

The experimental probability that John passed the quiz is 4/8, which simplifies to 1/2 or 0.5 (50%).

To find the experimental probability that John passed the quiz, we should follow these steps:

1. Determine the criteria for passing the quiz: John needs to have at least 3 correct answers to pass.

2. Identify John's method: Odd numbers stand for True, and even numbers stand for False.

3. Check the correct answers' pattern: True (T), True (T), False (F), False (F), and True (T).

4. Analyze each trial to see if the pattern of True (odd numbers) and False (even numbers) matches the correct pattern.

5. Count the number of trials in which John passed the quiz (3 or more correct answers).

6. Calculate the experimental probability by dividing the number of trials passed by the total number of trials.

Now, let's analyze each trial:

• Trial 1: Random numbers are 22 (F), 33 (T), 18 (F), 45 (T), 80 (F). The pattern is F, T, F, T, F. Compared to the correct pattern T, T, F, F, T, there is only one match (the third question). Result: Fail.
• Trial 2: Random numbers are 11 (T), 3 (T), 72 (F), 98 (F), 67 (T). The pattern is T, T, F, F, T. This matches the correct pattern exactly. Result: Pass.
• Trial 3: Random numbers are 28 (F), 36 (F), 43 (T), 85 (T), 71 (T). The pattern is F, F, T, T, T. Compared to the correct pattern T, T, F, F, T, there are two matches (the fourth and fifth questions). Result: Fail.
• Trial 4: Random numbers are 27 (T), 56 (F), 41 (T), 12 (F), 90 (F). The pattern is T, F, T, F, F. Compared to the correct pattern T, T, F, F, T, there are three matches (the first, third, and fourth questions). Result: Pass.
• Trial 5: Random numbers are 20 (F), 59 (T), 31 (T). The pattern is F, T, T. We only have three numbers here, but since the correct pattern starts with T, T, F, there is only one match (the third question). Result: Fail.
• Trial 6: Random numbers are 11 (T), 7 (T), 50 (F), 18 (F), 82 (F). The pattern is T, T, F, F, F. Compared to the correct pattern T, T, F, F, T, there are four matches (the first, second, third, and fourth questions). Result: Pass.
• Trial 7: Random numbers are 17 (T), 44 (F), 76 (F), 39 (T), 20 (F). The pattern is T, F, F, T, F. Compared to the correct pattern T, T, F, F, T, there are three matches (the first, third, and fourth questions). Result: Fail.
• Trial 8: Random numbers are 2 (F), 93 (T), 53 (T), 38 (F), 29 (T). The pattern is F, T, T, F, T. Compared to the correct pattern T, T, F, F, T, there are three matches (the second, third, and fifth questions). Result: Pass.

John passed 4 out of 8 trials. Therefore, the answer is 4/8, which simplifies to 1/2 or 0.5 (50%).

The complete question is here:

Answer 2

The experimental probability that John passed the quiz is 1/2 or 0.5. The trials conducted, John passed the quiz 50% of the time. ​

How do we find the experimental probability?

The correct answers for the quiz are T, T, F, F, T.

He decides that odd numbers generated by the calculator will represent "True" and even numbers will represent "False."

He performs 8 trials and records the results.

Trial 1: Fail (2 correct)

Trial 2: Pass (3 correct)

Trial 3: Fail (2 correct)

Trial 4: Pass (4 correct)

Trial 5: Fail (1 correct)

Trial 6: Pass (3 correct)

Trial 7: Fail (2 correct)

Trial 8: Pass (3 correct)

we can calculate the experimental probability by dividing the number of successful trials (those where John passed) by the total number of trials.

4/8 = 1/2