Predict Approximate Probability
1.
Andrea has a bag of 50 Starbursts of different colors. She picks one out of the bag and then replaces it. In her experiment she did the drawing 10 times. She drew 3 pink, 2 orange, 4 red, and 1 yellow. If this sample represents the colors in the bag, what number of each color Starburst do you predict is in the bag?
2.
Richard spins the spinner 100 times.
The 1 wedge three times as large as the 3, 4 or 5 wedge. The 2 wedge twice as large as the wedge 5, 4 or 3. About how many times would you expect Richard to spin a 2?
3.
A penny is flipped 10 times in an experiment. It flips to heads 8/10 times. What is the difference between this experimental probability and the theoretical probability of flipping a penny and landing heads?
4.
Jenny has 5 cards: blue, yellow, orange, red, and brown. In an experiment she draws one, records the color, puts the card back and reshuffles. In her experiment, she drew 100 times and drew brown 25 times. Which statement is true about this event: a.
Jenny’s results are the same as the predicted results. b.
Jenny’s results are higher than one would predict based on theoretical probability. c.
Jenny’s results are lower than one would predict based on theoretical probability.

Explanation:
4.
This problem expects you to assume some things. What I mean is that you are supposed to assume that the 10 starbursts you pick show the exact proportions of each color to the whole. For example, 1 yellow Starburst was chosen out of 10. That means, if you had 20 Starbursts from this bag, you would expect to pick twice as many yellow: 2 yellow. If you picked 30, you would expect to pick 1 yellow for every 10, which is 3.
(There are three tens in 30). So basically you set up a equal proportion like this:
1 yellow Starburst = ________yellow Starbursts
10 Starbursts 50 Starbursts.
Well, 10 x 5 is 50 so if I want to create equal proportions I need to multiply the numerator and denominator by 5. So 1 x 5 is 5. Therefore, I predict that 5 yellow
Starbursts will be picked out of 50. 5/50.
If you set up each color in the same way, you’ll realize that since the big bag has 50, you have to multiple each color by 5 since you only picked out of ten. j
5.
The first part of this problem is to calculate the theoretical probability of rolling each number. Spinners help us see probability as fractions. Look at the number 2 wedge.
What fraction does it look like of the circle?..... It looks like ¼ of the circle, so I’d guess that the theoretical probability of spinning a 2 is ¼. However, we really need to verify.
After reading the question two times, I realized it said that wedge 1 was 3 times larger than wedge 4,5 or 3. This means that wedge 3, 4, and 5 are the same size. This also means that wedge 1 can be split into 3 pieces and each of those pieces would be the same size as the little wedges.
The other information says that wedge 2 is twice as large as the little wedges. So I could break up wedge 2 into two equal pieces. Now, everything is divided in pieces the same size as the little wedges. If you count all the wedges up, you’ll get 8 equal pieces.
Then I look at wedge 2, and it has two equal pieces out of the 8. So the probability of spinning a 2 is 2/8 which can be simplified to ¼.
Now, I know the theoretical probability of rolling a 2 is ¼ as predicted. So, what is the predicted amount of times I’ll spin a 2 when I do it 100 times. Well, ¼ of 100 I should spin 2’s. So what is ¼ of a 100 – that is ¼ x 100 which is the same as 100/4 which equals 25. So if the experiment went according to the theoretical probability, we would spin the 2 wedge 25 times out of 100 or 25/100 or 25%.
6.
We already know the experimental probability was 8/10 times. So, we need to calculate how many times the coin was expected to flip heads, which requires us to calculate the theoretical probability. The theoretical probability is the specified outcome all the possible outcomes

So in this case heads is 1 specified outcome out of 2 possible outcomes (heads or tails).
So the theoretical probability of flipping a heads is ½. Since there were 10 trials, we would expect ½ of those to be heads. ½ of 10 is 5 so we’d expect 5/10 to be heads. The difference between 8/10 and 5/10 is 3/10 because 8/10- 5/10 = 3/10.
7.
There are five cards so the theoretical probability of any of them being drawn is 1/5.
So the probability of drawing brown each time is 1/5. Now in her experiment of 100 trials, she drew brown 25/100 times. We can simplify that fraction to ¼. So, the experimental probability is greater than the theoretical probability because ¼ is greater than 1/5.