determine the sample space of rolling a pair of dice and random variable D in getting the sum of numbers. Then, construct the discrete probability distribution and histogram
Question
determine the sample space of rolling a pair of dice and random variable D in getting the sum of numbers. Then, construct the discrete probability distribution and histogram
Solution
Step 1: Determine the Sample Space
The sample space of rolling a pair of dice is all the possible outcomes that can occur. Since a die has 6 faces, rolling two dice can result in 36 possible outcomes. These are all combinations of two numbers from 1 to 6.
Step 2: Define the Random Variable D
The random variable D is defined as the sum of the numbers on the two dice. This can take on any value from 2 (if both dice show 1) to 12 (if both dice show 6).
Step 3: Construct the Discrete Probability Distribution
The discrete probability distribution of D is a list of probabilities associated with each of its possible values. It is calculated by dividing the number of outcomes that result in each value of D by the total number of outcomes.
Here is the distribution:
- D=2: 1/36
- D=3: 2/36
- D=4: 3/36
- D=5: 4/36
- D=6: 5/36
- D=7: 6/36
- D=8: 5/36
- D=9: 4/36
- D=10: 3/36
- D=11: 2/36
- D=12: 1/36
Step 4: Construct the Histogram
The histogram is a graphical representation of the distribution. On the x-axis, you plot the possible values of D (from 2 to 12). On the y-axis, you plot the probabilities associated with each value. The height of each bar corresponds to the probability of each outcome.
For example, the bar for D=7 would be the tallest since 7 has the highest probability of occurring (6/36), while the bars for D=2 and D=12 would be the shortest since these outcomes have the lowest probabilities (1/36).
Similar Questions
Two dice are rolled and the sum is recorded.(a) List all possible outcomes (i.e. the sample space).(b) Calculate the probability of rolling:(i) A sum of 5(ii) A sum of 4 or less(iii) A sum of at most 11(iv) A sum that is a multiple of 3 or a multiple of 4
Imagine rolling a six sided die, the sample space isa. {1, 2, 3, 4}b. {1, 2, 3, 4, 6}c. {1, 2, 3, 4, 5, 6}d. {1, 2}
a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?1, 2, 3, 4, 5, 6; not equally likely0, 1, 2, 3, 4, 5, 6; not equally likely 1, 2, 3, 4, 5, 6; equally likely0, 1, 2, 3, 4, 5, 6; equally likely(b) Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.)Outcome Probability1 2 3 4 5 6 Do the probabilities add up to 1? Should they add up to 1? Explain.Yes, but they should not because these values do not cover the entire sample space.Yes, because these values cover the entire sample space. No, because these values do not cover the entire sample space.No, but they should because these values cover the entire sample space.(c) What is the probability of getting a number less than 2 on a single throw? (Enter your answer as a fraction.)(d) What is the probability of getting 1 or 2 on a single throw? (Enter your answer as a fraction.)
What is the sample space of a six-sided dice roll? 5 5 1 1 to 6 6 1 1 and 6 Infinity
You roll a fair four-sided die and a fair six-sided die. Find the number of possible outcomes in the sample space.The number of possible outcomes in the sample space is .
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