A coin has one of two outcomes: heads or tails. Each has an equal probability of occurring, meaning that they each have a 50% chance to occur. (They need to add up to 100% because they include all the outcomes, divide that into two equal parts and...)
This is what we call theoretical probability. It's a guess as to how probability <em>should</em> work. Like in the experiment, it's not always going to be 50-50.
What <em>actually happens</em> is called experimental probability. This may vary slightly from theoretical probability because you can't predict probability with complete certainty, you can only say what is <em>most likely to happen</em>.
We want to find the probability of getting heads in our experiment so we can compare it to the theoretical outcome. To do this, we need to compare the number of heads to the total number of outcomes.
We have 63 heads, and a total of 150 coin flips. That makes the probability of getting a heads 63/150. The hard part is getting this ratio into a percent.
You can try simply dividing, but you should be able to notice something here. SInce the top and the bottom of our fraction are both divisible by 3, we can <em>simiplify</em>. 63 ÷ 3 = 21 150 ÷ 3 = 50 So we could say that 63/150 = 21/50.
A percent is basically a fraction out of 100. Just like you can divide the parts of a ratio by the same number and it will stay the same, you can also multiply. To get the fraction out of 100, let's multiply by 2. (since 50 × 2 = 100)
21 × 2 = 42 50 × 2 = 100 21/50 = 42/100 = 42%
Comparing our experimental probability to the theoretical one...it is 8% lower.
This is complicated because the scales on the x-axis and y-axis are not the same. Graph D has the correct y-intercepts and the correct slopes. The solution is x = 500, where the two lines intersect.
