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1-8.3 A pair of dice are rolled. Let A be the event of obtaining an odd number on the first die and B be the event of obtaining and odd number on the second die. Let C be the event of obtaining an odd total from both dice. a) Show that A and B are independent, that A and Care independent, and that B and C are independent. b) Show that A, B, and C are not mutually independent.

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

 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. What is the probability of obtaining a value of 7?

c. What is the probability of obtaining a value of 7?

d. What is the probability of obtaining a value of 9 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.

f. What method did you use to assign the probabilities requested?

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. What is the probability of obtaining a value of 7?

c. What is the probability of obtaining a value of 7?

d. What is the probability of obtaining a value of 9 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.

f. What method did you use to assign the probabilities requested?

 

Suppose two dice (one red, one green) are rolled.

Consider the following events. A: the red die shows 1; B: the number add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 11. In express the stated event in symbolic form and say how many elements it contains [Hint: See Example]

The red die shows 1, but numbers do not add to 11.

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