When flipping a fair coin 50 times, you get 32 heads and 18 tails. What is the experimental probability of getting heads?

Question

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1 point
32/50 or 0.64
18/50 or 0.36
1/2 or 0.50
25/50 or 0.50
In a bag of marbles, there are 3 red, 4 blue, and 5 green marbles. What is the theoretical probability of drawing a blue marble?
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1 point
5/12
4/12
4/3
2/3
A spinner is divided into equal sections numbered 1 through 8. What is the theoretical probability of landing on an even number?
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1 point
3/8
1/8
4/8
5/8
After rolling a fair six-sided die 100 times, you get the number 3 exactly 20 times. What is the experimental probability of rolling a 3?
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1 point
1/6
2/5
20/100
80/100
What is the main difference between experimental and theoretical probability?
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1 point
Experimental probability uses actual results, while theoretical uses expected results
Theoretical probability is always more accurate
Experimental probability is always more accurate
They always give the same results
If you flip a fair coin 1000 times, which outcome would you expect?
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1 point
Exactly 500 heads and 500 tails
Around 400 heads and 600 tails
Close to 500 heads and 500 tails
All heads or all tails
A bag contains 20 identical balls numbered 1 to 20. What is the theoretical probability of drawing a number divisible by 5?
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1 point
1/5
4/20
5/20
3/4
In an experiment, a student spins a spinner 40 times and lands on red 12 times. If the spinner has only red and blue sections, what is the experimental probability of landing on blue?
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1 point
12/40
28/40
1/2
3/10
As you increase the number of trials in an experiment, what typically happens to the experimental probability?
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1 point
It becomes more random
It gets farther from the theoretical probability
It gets closer to the theoretical probability
It stays exactly the same
If the theoretical probability of an event is 1/3, what would be the expected number of successes in 90 trials?
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1 point
20
30
40
45
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Answer 1

Let's go through each question step by step:

1. Experimental probability of getting heads when flipping a fair coin 50 times:

   • You got 32 heads out of 50 flips.
   • The experimental probability of getting heads = Number of heads / Total flips = 32/50 = 0.64

2. Theoretical probability of drawing a blue marble from a bag containing 3 red, 4 blue, and 5 green marbles:

   • Total marbles = 3 + 4 + 5 = 12
   • The probability of drawing a blue marble = Number of blue marbles / Total marbles = 4/12 = 1/3 (which happens to be the simplest form)

3. Theoretical probability of landing on an even number from a spinner divided into 8 equal sections (1 to 8):

   • Even numbers: 2, 4, 6, 8 (4 even numbers)
   • Total sections = 8
   • The probability = Number of even numbers / Total sections = 4/8 = 1/2

4. Experimental probability of rolling a 3 after rolling a fair six-sided die 100 times:

   • You rolled a 3 exactly 20 times.
   • The experimental probability = Number of times 3 is rolled / Total rolls = 20/100 = 0.2 = 1/5

5. Main difference between experimental and theoretical probability:

   • Experimental probability uses actual results, while theoretical uses expected results. (Correct answer)

6. Expected outcome when flipping a fair coin 1000 times:

   • You would expect close to 500 heads and 500 tails. (Correct answer)

7. Theoretical probability of drawing a number divisible by 5 from numbered balls 1 to 20:

   • Numbers divisible by 5: 5, 10, 15, 20 (4 numbers)
   • Total numbers = 20
   • The probability = Number of suitable outcomes / Total outcomes = 4/20 = 1/5

8. Experimental probability of landing on blue when landing on red 12 times out of 40 spins:

   • Total spins = 40
   • If red was landed on 12 times, then blue was landed on 40 - 12 = 28 times.
   • Experimental probability of landing on blue = 28/40 = 0.7 (which simplifies to 7/10)

9. As you increase the number of trials in an experiment, what typically happens to the experimental probability?

   • It gets closer to the theoretical probability. (Correct answer)

10. If the theoretical probability of an event is 1/3, what would be the expected number of successes in 90 trials?

    • Expected successes = Probability * Total Trials = (1/3) * 90 = 30

Let me know if you have any more questions!