Question

Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. (a) How many sample points are possible? (Hint: use the counting rule for multiple-step experiments.) (b) List the sample points. There to sum the face values of a pair of dice to 2. There to sum the face values of a pair of dice to 3. There to sum the face values of a pair of dice to 4. There to sum the face values of a pair of dice to 5. There to sum the face values of a pair of dice to 6. There to sum the face values of a pair of dice to 7. There to sum the face values of a pair of dice to 8. There to sum the face values of a pair of dice to 9. There to sum the face values of a pair of dice to 10. There to sum the face values of a pair of dice to 11. There to sum the face values of a pair of dice to 12. (c) What is the probability of obtaining a value of 5? (d) What is the probability of obtaining a value of 8 or greater? (e) Because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain. This statement correct because P(odd) = and P(even) = . (f) What method did you use to assign the probabilities requested? classical method empirical method subjective method relative frequency method

Answer 1

Answer:

a.) 21

b.)

c.) 2/21

d.) 3/7

e.) Yes

f.) relative frequency method.

Step-by-step explanation:

Possible sample space if we are interested in only the sum becomes :

[1,1] [1,2] [1,3] [1,4] [1,5] [1,6]

[2,2] [2,3] [2,4] [2,5] [2,6]

[3,3] [3,4] [3,5] [3,6]

[4,4] [4,5] [4,6]

[5,5] [5,6]

[6,6]

a) there are 21 sample points.

b.) sample points to give sum of "2" = [1,1]

Sample points to give sum of "3" = [1,2]

Sample points to give sum of "4" = [1,3] [2,2]

Sample points to give sum of "5" = [1,4] [2,3]

Sample points to give sum of "6" = [1,5] [2,4] [3,3]

Sample points to give sum of "7" = [1,6] [2,5] [3,4]

Sample points to give sum of "8" = [2,6] [3,5] [4,4]

Sample points to give sum of "9" = [3,6] [4,5]

Sample points to give sum of "10" = [4,6] [5,5]

Sample points to give sum of "11" = [5,6]

Sample points to give sum of "12" = [6,6]

c.) probability of obtaining a value of 5 = favourable outcome/possible outcome = 2/21

d.) Probability of obtaining a value of 8 or greater = 9/21 = 3/7.

e.) Yes I agree with the statement because its only logical that since there are more values of even numbers than odd numbers, then we will see more of even than odd numbers.

f.) relative frequency method was used to assign the probabilities because we are dealing with the number of occurrence of a particular sum value.