Two cubes are rolled .both cubes are labelled 1 to 6.the number rolled are added.
What is the probability of each out come ?
a) sum is 12
B)the sum is less than 4.
C)the sum is 7.
D)the sum is 2.
Simply make a list of possibilities for each of your outcomes
I will do C)
To get a sum of 7 we could have:
16 25 34 43 52 or 61 for a totol of 6 cases
so prob(sum of 7) = 6/36 = 1/6
do the others the same way.
where did we get 36??
To determine the probability of each outcome, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, the total number of possible outcomes is 6 * 6 = 36.
a) Sum is 12:
There is only 1 outcome where both cubes show 6. Therefore, the probability is 1/36.
b) Sum is less than 4:
There are 3 outcomes where the sum is less than 4: (1, 1), (1, 2), and (2, 1). Therefore, the probability is 3/36, which simplifies to 1/12.
c) Sum is 7:
There are 6 outcomes where the sum is 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability is 6/36, which simplifies to 1/6.
d) Sum is 2:
There is only 1 outcome where both cubes show 1. Therefore, the probability is 1/36.
So, the probabilities are:
a) 1/36
b) 1/12
c) 1/6
d) 1/36
To find the probability of each outcome, we need to determine the number of ways each outcome can occur and divide it by the total number of possible outcomes.
First, let's calculate the total number of possible outcomes when rolling two dice labelled from 1 to 6. Since each die has 6 possible outcomes, the total number of outcomes is 6 * 6 = 36.
a) Sum is 12:
There is only one way to get a sum of 12, which is rolling two sixes (6 + 6). Therefore, the probability of this outcome is 1/36.
b) Sum is less than 4:
To calculate this probability, we need to determine the number of ways to get a sum less than 4. The possible combinations are (1,1), (1,2), (2,1), (1,3), and (3,1), which gives us a total of 5 possibilities. Therefore, the probability is 5/36.
c) Sum is 7:
To get a sum of 7, we have the following combinations: (1,6), (6,1), (2,5), (5,2), (3,4), and (4,3), which gives us a total of 6 possibilities. Therefore, the probability is 6/36, or simplified, 1/6.
d) Sum is 2:
To get a sum of 2, only one combination is possible, which is rolling two ones (1 + 1). Therefore, the probability is 1/36.
In summary:
a) Probability of sum being 12: 1/36
b) Probability of sum being less than 4: 5/36
c) Probability of sum being 7: 1/6
d) Probability of sum being 2: 1/36