if two fair dice are rolled what is the probability that the total showing is more than four?
Will you please explain how to do this problem?
Thank you
sum of 2 : 1 --(1,1)
sum of 3 : 2 -- (1,2) (2,1)
sum of 4 : 3 -- (1,3) (3,1) (2,2)
So sum of 4 or less : 6 of them
Then the number of tosses with a sum greater than 4 is 30 (there are 36 possible cases)
prob(of your event) = 30/36 = 5/6
Well, I'll roll up my sleeves and explain it to you, my friend! When two fair dice are rolled, we need to find the probability that the total showing is more than four.
To do this, let's first start by finding all the possible outcomes. Since we have two dice, each dice has 6 sides, so the total number of outcomes is 6 * 6 = 36.
Now, let's focus on the outcomes where the total showing is more than four. There are several ways this can happen: (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), and (6, 6).
In total, there are 23 outcomes that have a total more than four. So, the probability is 23/36, which can be simplified if needed.
Hope that clears things up for you! Feel free to roll any more questions my way.
To find the probability that the total showing on two fair dice is more than four, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes for rolling two dice.
Each die has six possible outcomes (numbers 1 to 6). Since there are two dice, the total number of outcomes is 6 x 6 = 36.
Step 2: Determine the number of outcomes where the total is more than four.
To find this, we can create a table of all possible outcomes and mark the favorable outcomes.
| Die 1 | Die 2 | Total |
|-------|-------|-------|
| 1 | 1 | 2 |
| 1 | 2 | 3 |
| 1 | 3 | 4 |
| 1 | 4 | 5 |
| 1 | 5 | 6 |
| 1 | 6 | 7 |
| 2 | 1 | 3 |
| 2 | 2 | 4 |
| 2 | 3 | 5 |
| 2 | 4 | 6 |
| 2 | 5 | 7 |
| 2 | 6 | 8 |
| 3 | 1 | 4 |
| 3 | 2 | 5 |
| 3 | 3 | 6 |
| 3 | 4 | 7 |
| 3 | 5 | 8 |
| 3 | 6 | 9 |
| 4 | 1 | 5 |
| 4 | 2 | 6 |
| 4 | 3 | 7 |
| 4 | 4 | 8 |
| 4 | 5 | 9 |
| 4 | 6 | 10 |
| 5 | 1 | 6 |
| 5 | 2 | 7 |
| 5 | 3 | 8 |
| 5 | 4 | 9 |
| 5 | 5 | 10 |
| 5 | 6 | 11 |
| 6 | 1 | 7 |
| 6 | 2 | 8 |
| 6 | 3 | 9 |
| 6 | 4 | 10 |
| 6 | 5 | 11 |
| 6 | 6 | 12 |
From the table, we can see that there are 21 favorable outcomes (total is more than four).
Step 3: Calculate the probability.
To get the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 21 / 36
Simplifying the fraction gives us:
Probability = 7 / 12
So, the probability that the total showing on two fair dice is more than four is 7/12.
To find the probability that the total showing is more than four when two fair dice are rolled, we need to first determine the total number of possible outcomes and then count the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes.
When two fair dice are rolled, each die can show one of six possible outcomes (numbers 1 through 6). Since there are two dice, the total number of possible outcomes is calculated as 6 * 6 = 36.
Step 2: Count the number of favorable outcomes.
We want to find the outcomes where the total showing is more than four. One way to approach this is to consider the outcomes where the sum of the numbers on the two dice is less than or equal to four and subtract it from the total number of possible outcomes.
To make this easier, we can create a table showing all the possible outcomes and the sum of the two numbers rolled:
| 1 2 3 4 5 6
-----------------------------
1 | 2 3 4 5 6 7
2 | 3 4 5 6 7 8
3 | 4 5 6 7 8 9
4 | 5 6 7 8 9 10
5 | 6 7 8 9 10 11
6 | 7 8 9 10 11 12
From the table, we can see that there are 9 outcomes where the sum is less than or equal to four: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (1, 4), (4, 1), and (2, 3).
Step 3: Calculate the probability.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 36 - 9 = 27
Probability = 27 / 36 = 3/4 = 0.75
Therefore, the probability that the total showing is more than four when two fair dice are rolled is 0.75 or 75%.