Melissa rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that the product of the numbers will be greater than or equal to 18? Write your answer in probability notation as a simplified fraction.
please help me!
how many pairs of numbers produce a product of at least 18?
36, 45 46, 54 55 56, 63 64 65 66 for a total of 10
So, P(ab >= 18) = 10/36
Possible products ≥ 18
18 = 3*6 or 6*3
19 : none
20: 4*5 or 5*4
21, 22, 23 : all none
24 : 6*4 or 4*6
25 : 5*5
26-29: none
30: 5*6 or 6*5
36 : 6*6
prob of each product is the same,
so
so the only products are 18, 20, 24, 25, 30, 36
prob( product of 2 numbers to be 18,20,24, or 30) = 8(1/36)
prob(25 or 36) = 2(1/36) = 1/18
prob(your event) = 8/36 + 1/18 = 5/18
You could construct a matrix of 6 rows and 6 columns, where each entry
would be the product of the row and column numbers.
counting all the products ≥ 18 would be 10
prob(your event) = 10/36 = 5/18
Don't know where one can get dice to have products of the numbers showing to be greater than 36.
To find the probability that the product of the numbers will be greater than or equal to 18 when rolling two number cubes, we need to determine the number of favorable outcomes (i.e., the number of ways in which the product is greater than or equal to 18) and the total number of possible outcomes.
Let's analyze the possible outcomes for each cube:
For the first cube, there are 6 possible outcomes since it has 6 sides labeled with the numbers 1 to 6.
For the second cube, there are also 6 possible outcomes since it is identical to the first cube.
To find the favorable outcomes, we need to identify the combinations that result in a product greater than or equal to 18.
The possible combinations are:
(3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)
Since we have 10 favorable outcomes, the probability can be calculated as:
Probability = Favorable outcomes / Total outcomes
Total outcomes = 6 x 6 = 36
Favorable outcomes = 10
Therefore, the probability that the product of the numbers will be greater than or equal to 18 is 10/36, which can be simplified to 5/18.