copy of the entire thing, ill put pictures in later
Wendy throws a dart at this square-shaped target:
A square is shown with sides labeled 10. A shaded circle is shown in the center of the square. The diameter of the circle is 2.
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer. (5 points)
Part A: The probability of hitting the black circle inside the target is closer to 0 because the circle is much smaller, which you can tell by just looking at it or doing the calculations. If you did the calculations, the black circle has an area of 3.14. The white portion has an area of 96.86. That is a 3% for the black circle and 97% for the white portion. 97% is much larger than 3%, and 3% is very close to 0, or 0%.
Part B: The probability of hitting the white portion of the target is closer to 1 because the white portion is much larger than the black circle. You can also see this by just looking at it, or by doing the calculations. If you did the calculations, the black circle has an area of 3.14. The white portion has an area of 96.86. That is a 3% for the black circle and 97% for the white portion. 97% is much larger than 3%, and 97% is very close to 1, or 100%.
Question 2 (Essay Worth 10 points)
(06.02 MC)
Alinn flipped a coin 20 times. The coin landed heads up 12 times and tails up 8 times.
Part A: Based on the results, what is the experimental probability of the coin landing heads up? Show your work. (5 points)
Part B: What is the theoretical probability of the coin landing heads up? Show your work. (5 points)
Part A: The experimental probability of the coin landing heads up is 60%. 12 / 20 = 0.6, or 60%
Part B: The theoretical probability of the coin landing heads up is 50%. Because there are two sides, you would need to divide 100 by 2, which equals 50, or 50%. It does not matter how many times you flip the coin, there will always be two sides of the coin, making the theoretical probability of getting heads always the same.
Question 3 (Essay Worth 10 points)
(06.04 MC)
Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results:
Position Open Side Up Closed Side Up Landing on Side
Number of Times Landed in Position 1 5 44
Based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). Show your work.
Open Side Up: The experimental probability is 2%.
1 / 50 = 0.02, or 2%
Closed Side Up: The experimental probability is 10%.
5 / 50 = 0.1, or 0.10, or 10%
Landing on Side: The experimental probability is 88%.
44 / 50 = 0.88, or 88%
Maria's experimental probability may be different from the theoretical probability of spinning a coin because the theoretical probability is just a guess. When we do theoretical probability, we are saying that every possibility has an equal chance of getting picked. The experimental probability is the actual results. The experimental probability is what happened, and may always be different.
Question 4 (Essay Worth 10 points)
(06.05 MC)
Maria spins a penny 100 times and it lands head side up 62 times. Explain why Maria's experimental probability may be different from the theoretical probability of spinning a coin.
Maria's experimental probability may be different from the theoretical probability of spinning a coin because the theoretical probability is just a guess. When we do theoretical probability, we are saying that every possibility has an equal chance of getting picked. The experimental probability is the actual results. The experimental probability is what happened, and may always be different.