Two tetrahedral dice are thrown; one is red and the other is blue . The number on which each lands is noted, the faces being marked 1,2,3,4. Find the probability that the sum of the numbers on which the dice lands is 6 given that the red die lands on an odd number.
if red is 1, blue has to be 5, can't happen
if red is 3 blue has to be 3
So only one case
prob (of stated event) = 1/4
To find the probability that the sum of the numbers on which the dice lands is 6 given that the red die lands on an odd number, we need to determine the favorable outcomes and the possible outcomes.
Let's first list the possible outcomes when rolling the two tetrahedral (four-sided) dice labeled 1, 2, 3, and 4.
The red die can land on either 1 or 3 since these are the odd numbers. For each of these possibilities, we will determine the number on which the blue die lands such that their sum is 6.
When the red die lands on 1, the possible outcomes for the blue die are:
- The blue die lands on 5, since 5 + 1 = 6.
- There is only one possible outcome in this case.
When the red die lands on 3, the possible outcomes for the blue die are:
- The blue die lands on 3, since 3 + 3 = 6.
- The blue die lands on 2, since 2 + 4 = 6.
- The blue die lands on 4, since 4 + 2 = 6.
- There are three possible outcomes in this case.
Therefore, the total number of favorable outcomes is 1 + 3 = 4.
Now let's find the total number of possible outcomes. Since there are four possible outcomes for both dice, the total number of possible outcomes is 4 * 4 = 16.
To calculate the probability, we will divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Number of Possible Outcomes
Probability = 4 / 16 = 1 / 4 = 0.25
Therefore, the probability that the sum of the numbers on which the dice lands is 6, given that the red die lands on an odd number, is 0.25 or 25%.
To find the probability that the sum of the numbers on which the dice land is 6 given that the red die lands on an odd number, we can use conditional probability.
First, let's find the probability that the red die lands on an odd number. A tetrahedral die has 4 faces, and there are 2 odd numbers (1 and 3) out of the 4 possible outcomes. So, the probability of the red die landing on an odd number is 2/4 or 1/2.
Now, let's consider the possibilities for the blue die. Since there are 4 faces, we can list the possible outcomes: (1,2), (2,1), (3,?), (?,3). We are looking for the combinations where the sum is 6. The only possible combination is (3,3).
So, out of the 4 possible outcomes for the two dice, only 1 outcome will result in a sum of 6 given that the red die lands on an odd number.
Therefore, the probability that the sum of the numbers on which the dice lands is 6, given that the red die lands on an odd number, is 1/4.
Note: It's important to note that the conditional probability is applied when we restrict the sample space based on a given condition, in this case, the red die landing on an odd number.