Hannah rolls two number cubes. What is the probability that both numbers are greater than 3?
One third
There are only 3 ways to get 3 or less:
1,1
1,2
2,1
So, there are 33 ways to get more than 3.
To find the probability that both numbers rolled on the two number cubes are greater than 3, we need to determine the total number of possible outcomes and the number of favorable outcomes.
1. Determine the total number of possible outcomes:
Since each number cube has 6 faces numbered 1 to 6, the total number of possible outcomes for rolling two number cubes is the product of the number of faces on each cube:
Total number of possible outcomes = 6 x 6 = 36
2. Determine the number of favorable outcomes:
We want both numbers rolled to be greater than 3, so we need to count the number of outcomes where both numbers satisfy this condition.
The favorable outcomes are:
(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)
So, there are 9 favorable outcomes.
3. Calculate the probability:
The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 9 / 36
Therefore, the probability that both numbers rolled on the two number cubes are greater than 3 is 9/36, which simplifies to 1/4 or 0.25.