Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for rolling it once. Your probability model shows a probable outcome of 1/6 for each of the numbers on the cube. 1 chance for all any of the 6 numbers.

1) If the equally likely model was correct, each outcome/number would turn up about 83 times each, in 500 rolls of the number cube.

2) Based on data from the roll of the number cube, Odd numbers turn out 0.456 or 45.6% of the time and even numbers turn out 0.544 or 54.4% of the time.

Step-by-step explanation:

Complete Question

Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for rolling it once. Your probability model shows a probable outcome of 1/6 for each of the numbers on the cube. 1 chance for all any of the 6 numbers.

Suppose your teacher allows you to roll it 500 times, and you get the following results:

Outcome 1 2 3 4 5 6

Frequency 77 92 75 90 76 90

Exercises 1–2

1. If the equally likely model was correct, about how many of each outcome would you expect to see if the cube is rolled 500 times?

2. Based on the data from the 500 rolls, how often were odd numbers observed? How often were even numbers observed?

Solution

1) If the equally likely model was correct,

The probability of rolling any of the numbers from 1 to 6 = p = (1/6)

The number of each of the outcomes expected to be seen in 500 rolls of the number cube = np = 500 × (1/6) = (500/6) = 83.333 ≈ 83

2) Based on data from the roll,

The odd numbers, 1, 3 and 5, were obtained 77, 75 and 76 times respectively.

Total number of times odd number were rolled = 77 + 75 + 76 = 228

Probability of an event is the number of elements in that event divided by the total number of events.

Probability of an odd number turning up

= (228/500) = 0.456 = 45.6%

The even numbers, 2, 4 and 6, were obtained 92, 90 and 90 times respectively.

Total number of times even number were rolled = 92 + 90 + 90 = 272

Probability of an even number turning up

= (272/500) = 0.544 = 54.4%

Hope this Helps!!!