Predicting vs. Observing Probability Examples

A die was rolled 50 times. These are the results:

6 5 4 5 4 1 3 4 2 6 2 6 1 6 6 4 2 4 5 5 1 1 1 5 3
3 3 1 5 3 6 1 4 1 4 2 3 3 1 2 6 6 4 3 6 6 5 4 2 2

a) What is the experimental probability of rolling each number? 

b) And how do these compare to the theoretical probabilities?

a) Out of fifty rolls of the die:

1 appears nine times; 2 appears seven times; 3 appears eight times; 4 appears nine times; 5 appears seven times; and 6 appears ten times

Thus, the experimental probability is as follows:

b) Now let's compare these to the theoretical probabilities. Each number is equally likely to be rolled, so each has a theoretical probability of ⅙ or about 16.7%. The experimental probabilities are close to this; some are slightly higher and some are slightly lower.

Rowan drew a marble from this bag, recorded the color (blue, green, or orange), then replaced it and drew again. She did this forty times. Here are the results:

g g g b b g g o g b
b b g o g b o g o o
b b g o g g b g b o
g b g o g o g g o o

Make a chart comparing the experimental and theoretical probabilities of drawing each color.

Jermain and Tremain both calculate the predicted probability of getting heads if they flip a coin 10 times. Then they each flip a coin 10 times.

a. Will they get the same number when they calculate the predicted probability?

b. When they actually flip the coin 10 times, will they get as many as the probability predicted, for sure, no matter what?

c. When they actually flip the coin 10 times, will Jermain absolutely, positively get the same number of heads as the Tremain?

a. Since they’re using the same formula to find the predicted probability, they will get the same number: .

b. The number of heads they flip is all up to chance. They should flip about 5 heads out of their 10 flips, but there’s no promise, no absolute way of knowing. The answer is no, there is no guarantee that they’ll flip 5 heads.

c. Because what they actually flip is up to chance, there is also no guarantee that Jermain will flip the same number of heads and the same number of tails as Tremain. It’s just flippin’ up to chance.