Two Dice, one red and one white are rolled, what is the probability that the white die turns up a smaller than the red die ?
36 possibilities total
white = 1 ---> 5 with white smaller
white = 2 --> 4
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white = 5 --> 1
In other words
5+4+3+2+1 = 15 out of 36
15/36 = .417
Well, the probability of the white die turning up smaller than the red die depends on the total number of possible outcomes. Since each die has 6 sides, the total number of outcomes when rolling two dice is 6 x 6 = 36.
Now, let's figure out the number of outcomes where the white die turns up smaller than the red die. We can start by listing all the possible outcomes:
White: 1, Red: 2
White: 1, Red: 3
White: 1, Red: 4
White: 1, Red: 5
White: 1, Red: 6
White: 2, Red: 3
White: 2, Red: 4
White: 2, Red: 5
White: 2, Red: 6
White: 3, Red: 4
White: 3, Red: 5
White: 3, Red: 6
White: 4, Red: 5
White: 4, Red: 6
White: 5, Red: 6
Counting the outcomes, we have 15 cases out of the total 36 cases where the white die turns up smaller than the red die.
So, the probability is 15/36, which simplifies to 5/12, which can also be interpreted as approximately 41.67% chance.
Now, that's just the math part. But hey, in the grand scheme of life, who doesn't like being a little rebellious? So, here's to the white die trying to be smaller, defying the odds!
To find the probability that the white die turns up smaller than the red die, we can consider the different outcomes when rolling the dice.
There are 6 possible outcomes for each die, as there are 6 sides on each die. Therefore, the total number of possible outcomes when rolling the two dice is 6 x 6 = 36.
Out of these 36 possible outcomes, we want to determine the number of outcomes where the white die turns up smaller than the red die.
Let's consider the cases where the white die is smaller than the red die:
1. White Die: 1, Red Die: 2, 3, 4, 5, or 6 (5 favorable outcomes)
2. White Die: 2, Red Die: 3, 4, 5, or 6 (4 favorable outcomes)
3. White Die: 3, Red Die: 4, 5, or 6 (3 favorable outcomes)
4. White Die: 4, Red Die: 5 or 6 (2 favorable outcomes)
5. White Die: 5, Red Die: 6 (1 favorable outcome)
Adding up the favorable outcomes, we have a total of 5 + 4 + 3 + 2 + 1 = 15 favorable outcomes.
Therefore, the probability that the white die turns up smaller than the red die is 15/36, which simplifies to 5/12 or approximately 0.4167.
To determine the probability that the white die turns up smaller than the red die when rolling two dice, we need to consider all possible outcomes and count how many of them satisfy the given condition.
Step 1: Determine the sample space
The sample space is the set of all possible outcomes when rolling two dice. Each die can have 6 possible outcomes (numbers 1-6), so the total number of outcomes is 6 × 6 = 36.
Step 2: Count the favorable outcomes
In this case, we want the white die to turn up smaller than the red die. To achieve this, we need to count the number of outcomes where the white die shows a number less than the number on the red die.
Let's list down all such outcomes:
- White: 1, Red: 2
- White: 1, Red: 3
- White: 1, Red: 4
- White: 1, Red: 5
- White: 1, Red: 6
- White: 2, Red: 3
- White: 2, Red: 4
- White: 2, Red: 5
- White: 2, Red: 6
- White: 3, Red: 4
- White: 3, Red: 5
- White: 3, Red: 6
- White: 4, Red: 5
- White: 4, Red: 6
- White: 5, Red: 6
There are 15 favorable outcomes.
Step 3: Calculate the probability
The probability is the ratio of the number of favorable outcomes to the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 15 / 36
Simplifying the fraction, we get:
Probability = 5 / 12
Therefore, the probability that the white die turns up smaller than the red die is 5/12.