Please explain how to get the answer.I have now idea.
1.If you roll two fair dice,one red and one green,what is the probability of getting a 2 on the red die and a 3 on the green die? Give answer in a reduced fraction.
2.If you roll two fair dice,one red and one green,what is the probability that the sum of the two dice is 5? Give answer in a reduced fraction.
3.If you roll two fair dice,one red and one green,what is the probability of getting a leat one 6 on the two dice?Give answer in a reduced fraction.
1. prob = (1/6)(1/6) = 1/36
2. the colour does not matter
there are 4 ways to get a sum of 5
(1,4) (2,3) (3,2) (4,1)
prob = 4/36 = 1/9
3. Again, what does the colour have to do with it?
prog(no 6 showing) = (5/6)(5/6) = 25/36
prob(at least one 6) = 1 - 25/36 = 11/36
Find P(1 on green die and 3 on red die). (Enter your answer as a fraction.)
To get the answer to each of these questions, we need to understand some basic principles of probability.
1. Probability of getting a specific outcome on a single die:
When rolling a fair six-sided die, each face has an equal probability of landing face up. So, the probability of rolling a 2 on the red die is 1/6.
2. Probability of two independent events both happening:
When rolling two dice, the outcome on one die does not affect the outcome on the other. Therefore, to find the probability of both events happening, we can multiply the probabilities of each event individually.
For question 1, the probability of rolling a 2 on the red die is 1/6, and the probability of rolling a 3 on the green die is also 1/6. Multiplying these probabilities together, the probability of getting a 2 on the red die and a 3 on the green die is (1/6) * (1/6) = 1/36.
3. Probability of two dice sums:
To find the probability that the sum of two dice is a specific number, we need to determine the number of combinations that result in that sum. Then, we divide that number by the total number of possible outcomes.
For question 2, we need to find the number of combinations that result in a sum of 5. These combinations are (1, 4), (2, 3), (3, 2), and (4, 1). So, there are four possible outcomes that result in a sum of 5.
Next, we need to calculate the total number of possible outcomes when rolling two fair dice. Since each die has six faces, the total number of outcomes is 6 * 6 = 36.
Therefore, the probability of getting a sum of 5 is 4/36, which can be reduced to 1/9.
4. Probability of at least one 6:
To find the probability of getting at least one 6 when rolling two dice, we can use the concept of complementary events. We find the probability of the opposite event (getting no 6) and subtract it from 1.
The probability of not getting a 6 on a single die is 5/6 because there are five faces that are not a 6 out of the six total faces.
To find the probability of not getting a 6 on both dice, we multiply the probabilities together: (5/6) * (5/6) = 25/36.
Finally, we subtract this from 1 to get the probability of getting at least one 6: 1 - (25/36) = 11/36.