If two indistinguishable dice are rolled, what is the probability of the event {(2, 2), (3, 2), (1, 2)}?
1/12
To calculate the probability of the event {(2, 2), (3, 2), (1, 2)}, we need to determine how many favorable outcomes there are and divide it by the total number of possible outcomes.
First, let's determine the number of favorable outcomes:
There are three ways to roll a (2, 2) since both dice need to show a 2.
There is one way to roll a (3, 2) since one die needs to show a 3 and the other needs to show a 2.
There is one way to roll a (1, 2) since one die needs to show a 1 and the other needs to show a 2.
So, there are a total of 3 + 1 + 1 = 5 favorable outcomes.
Next, let's determine the total number of possible outcomes:
Since there are two dice, there are 6 possible outcomes for each dice roll.
Therefore, the total number of possible outcomes is 6 * 6 = 36.
Finally, let's calculate the probability:
The probability is given by the ratio of favorable outcomes to total outcomes.
Probability = (number of favorable outcomes) / (number of total outcomes)
= 5 / 36
So, the probability of the event {(2, 2), (3, 2), (1, 2)} is 5 / 36 or approximately 0.1389 (rounded to four decimal places).
To find the probability of the event {(2, 2), (3, 2), (1, 2)}, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
In this case, we have two indistinguishable dice, which means they are identical and have the same numbers on each face. Each die has six faces numbered from 1 to 6.
To calculate the total number of possible outcomes, we need to consider the number of choices for each die. Since there are six faces on each die, there are 6 * 6 = 36 possible outcomes.
Now let's identify the favorable outcomes. From the event {(2, 2), (3, 2), (1, 2)}, we can see that we are looking for the outcomes where the second die rolls a 2. The first die doesn't affect the outcome in this event. There are three favorable outcomes with the second die rolling a 2, which are (2, 2), (3, 2), and (1, 2).
So, the probability of the event {(2, 2), (3, 2), (1, 2)} is the ratio of the number of favorable outcomes to the total number of possible outcomes, which gives us 3/36.
Simplifying the fraction, we get 1/12. Therefore, the probability of the event {(2, 2), (3, 2), (1, 2)} is 1/12.