Question

Ashley rolled a number cube

500

times and got the following results.

Outcome Rolled	1	2	3	4	5	6
Number of Rolls	93	82	62	92	86	85

Fill in the table below. Round your answers to the nearest thousandth.

(a)	Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.
(b)	From Ashley's results, compute the experimental probability of rolling an odd number.
(c)	Assuming that the cube is fair, choose the statement below that is true:
	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 matter the number of rolls.
	The larger the number of rolls, the greater the likelihood that the experimental probability will be close to the theoretical probability.

Answer 1

a.) The possible outcomes of a cube roll are 1, 2, 3, 4, 5, 6. So the odd outcomes out of these are 1, 3, 5.

That means the theoretical probability of rolling an odd number

= No. of favorable outcomes in which we get an odd number/Total no. of  outcomes

= 3/6

= 0.5

b.) From her experiment of 500 rolls, Ashley observed the outcome 1 - 93 times, outcome 3 - 62 times, and outcome 5 - 86 times.

So, the experimental probability of rolling an odd number = (93 + 62 + 86) / 500 = 0.482

c.) The larger the number of rolls, the greater the likelihood that the experimental probability will be close to the theoretical probability.