Question

The experimental probability.

The table shows the outcomes of rolling two
number cubes at the same time and finding the
product of the two numbers.co
7. What is the theoretical probability, expressed as
a fraction, of rolling a product greater than 12?
1
1
2 2
3
3
4
5
6
Florida's B.E.S.T. Assessment Practice Workbook 2 of 2
لیا
4
5
6
2
2
4
6
800
10
12
3
3
6
9
12
15
12
16
20
24
15
20 25
30
18 24 30 36
4
4
8
80 2
5
5
10
8. If Alan rolls two number cubes 300 times, about how many times would he expect a
product greater than 10? Round to the nearest whole number.
6
6
12
18

Answer 1

7. To find the theoretical probability of rolling a product greater than 12, we need to count the number of outcomes where the product is greater than 12 and divide by the total number of possible outcomes.

From the table, we can see that the outcomes with a product greater than 12 are: (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), and (6, 6). This gives us a total of 15 outcomes with a product greater than 12.

The total number of possible outcomes is 6 x 6 = 36, since there are 6 possible outcomes for each of the two number cubes.

Therefore, the theoretical probability of rolling a product greater than 12 is 15/36, which simplifies to 5/12.

8. To find the approximate number of times Alan would expect to roll a product greater than 10 in 300 rolls, we can multiply the total number of rolls by the probability of rolling a product greater than 10.

From the table, we can see that the outcomes with a product greater than 10 are: (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (3, 4), (4, 3), (5, 2), (6, 2), (4, 2), (5, 2), and (6, 2). This gives us a total of 21 outcomes with a product greater than 10.

The probability of rolling a product greater than 10 is 21/36, which simplifies to 7/12.

Multiplying the total number of rolls (300) by the probability (7/12), we get:

300 x 7/12 = 175

So Alan would expect to roll a product greater than 10 about 175 times in 300 rolls.