Question

Lashonda rolled a number cube 500 times and got the following results.

Outcome Rolled
1
2
3
4
5
6
Number of Rolls
77
89
73
69
110
82
Answer the following. Round your answers to the nearest thousandths.
(a) From Lashonda's results, compute the experimental probability of rolling an odd number.
0
(b) Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.
0
(c) Assuming that the cube is fair, choose the statement below that is true.
O The larger the number of rolls, the greater the likelihood that the experimental probability
will be close to the theoretical probability.
O The smaller the number of rolls, the greater the likelihood that the experimental
probability
will be close to the theoretical probability.
The experimental probability will never be very close to the theoretical probability, no
X

Answer 1

Explanation:

if I understand this correctly, then

1 was rolled 77 times

2 89 times

3 73 times

4 69 times

5 110 times

6 82 times

remember, a probability is always desired cases over total possible cases.

a)

the experimental probability to roll an odd number (1, 3, 5) is the number of desired cases (77 + 73 + 110) over the total cases (500).

260 / 500 = 26/50 = 13/25 = 0.52

b)

if the cube would be totally equal, so that every side has truly the same probability to appear we would have for every roll 6 total possible outcomes (1 .. 6), and 3 desired outcomes (1, 3, 5).

so the theoretical probability is

3/6 = 1/2 = 0.5

c)

if the cube is truly "fair" (all sides really have the same probability to show), then the first answer is true.

the more rolls of the die, the greater the likelihood that both probabilities will get closer and closer.

that is actually a main point of probabilities : to find the most likely behavior or structure of a large number of items or objects out of the structure or behavior of a smaller sample. or out of theoretical considerations that can be tested with smaller samples.