Two dice are rolled. Find the probability that an even number is rolled on one die and an odd number is rolled on the second die.
You could have EO, or OE
prob(EO) = (/12)(1/2) = 1/4
prob(OE) = (/12)(1/2) = 1/4
so prob of one even one odd = 1/4 + 1/4 = 1/2
Another way:
make a chart with DIE1 on top and DIE2 on the side.
there will be 36 outcomes, 18 even sums and 18 odd sums.
(notice that the sum of an even + odd = odd, but the sum of either two evens or two odds is even)
so prob = 18/36 = 1/2
To find the probability of rolling an even number on one die and an odd number on the second die, we can first determine the total number of possible outcomes.
Since two dice are being rolled, each die has 6 possible outcomes (numbers 1 to 6). The total number of possible outcomes is thus 6 * 6 = 36.
Now, let's determine the favorable outcomes, i.e., the outcomes where one die shows an even number and the other die shows an odd number.
For the first die to show an even number, there are 3 possible outcomes (2, 4, or 6).
For the second die to show an odd number, there are also 3 possible outcomes (1, 3, or 5).
Since these events are independent, multiply the number of outcomes for each die: 3 * 3 = 9.
Therefore, the probability of rolling an even number on one die and an odd number on the second die is 9/36, which simplifies to 1/4 or 0.25.
To find the probability of rolling an even number on one die and an odd number on the second die, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
First, let's determine the possible outcomes for each die:
- There are 3 even numbers on a standard six-sided die: 2, 4, and 6.
- There are 3 odd numbers on a standard six-sided die: 1, 3, and 5.
To calculate the total number of possible outcomes, we multiply the number of possibilities for each die:
Total possible outcomes = Number of possibilities on the first die × Number of possibilities on the second die = 3 × 3 = 9.
Now, let's consider the favorable outcomes, which are the combinations where an even number is rolled on one die and an odd number is rolled on the second die:
- Out of the 3 even numbers on the first die, there are 3 choices for an odd number on the second die (1, 3, or 5).
- Similarly, out of the 3 odd numbers on the first die, there are 3 choices for an even number on the second die (2, 4, or 6).
So, the total number of favorable outcomes is 3 + 3 = 6.
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 6 / 9 = 2/3 or approximately 0.667.
Therefore, the probability of rolling an even number on one die and an odd number on the second die is 2/3 or approximately 0.667.