A six-sided-cube is labeled with the numbers 1, 2, 2, 3, 3, and 3. Four sides are colored red, one side is white, and one side is yellow. Find each probability.
Tossing 2, then 2.
Tossing red, then white, then yellow.
assistance needed
can you show me how to start
Prob(2, then another 2) = 2/6 * 2/6 = 1/9
Prob(red,white,yellow) = 4/6 * 1/6 * 1/6 = 1/54
these are the answers for them
For the first one there are 6 possible numbers, two of which are 2. So the probability of rolling a 2 is 2/6.
If these are independent then the probability of throwing another 2 is also 2/6.
The probability of the combined two events is the product of the probabilities thus
2/6*2/6 = 1/9
The same approach is taken for the coloured sides.
To find the probability of each scenario, we need to know the total possible outcomes and the favorable outcomes.
In the first scenario, we want to find the probability of tossing 2 and then 2. Let's calculate the total possible outcomes and the favorable outcomes:
Total possible outcomes: Since we are using a six-sided cube, there are 6 possible outcomes for each toss. Since we have 2 tosses, the total possible outcomes will be 6 multiplied by 6, which equals 36.
Favorable outcomes: We need to toss 2 and then 2. From the labels on the cube, we can see that there are two 2's. So, we have 2 favorable outcomes.
Therefore, the probability of tossing 2 and then 2 is 2/36, which simplifies to 1/18.
Now, let's move on to the second scenario, where we want to find the probability of tossing red, then white, then yellow.
Total possible outcomes: Since the cube has 6 sides, there are 6 possible outcomes for each toss. Therefore, the total possible outcomes will be 6 multiplied by 6 multiplied by 6, which equals 216.
Favorable outcomes: We want to toss red, white, and then yellow. From the information given, there are 4 red sides, 1 white side, and 1 yellow side. Therefore, there are 4 possible outcomes for the first toss, 1 possible outcome for the second toss, and 1 possible outcome for the third toss. Multiplying these together, we get 4 multiplied by 1 multiplied by 1, which equals 4.
Therefore, the probability of tossing red, then white, then yellow is 4/216, which can be simplified to 1/54.
To summarize:
1. The probability of tossing 2 and then 2 is 1/18.
2. The probability of tossing red, then white, then yellow is 1/54.