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Chapter 2: Q. 2.23 (page 50)

A pair of fair dice is rolled. What is the probability that the second die lands on a higher value than does the first?

Short Answer

Expert verified

512count the number of equally likely events.

Step by step solution

01

Given Information.

A pair of fair dice is rolled.

02

Explanation. 

Experiment: Two fair dice are rolled.

Question:P(seconddielandsonabiggernumber)=?

Since the dice are fair and distinct, each of the 6·6rolls is equally likely.

To enumerate the number of possible configurations in the wanted event, choose two out of 6the numbers - in 62ways. (Because each of these choices corresponds to one throw where the second dice gets a higher number)

P(second die scores higher)=626·6=1536=512

512count the number of equally likely events.

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Most popular questions from this chapter

An urn contains 5red, 6blue, and 8green balls. If a set of 3balls is randomly selected, what is the probability that each of the balls will be

(a) of the same color?

(b) of different colors? Repeat under the assumption that whenever a ball is selected, its color is noted and it is then replaced in the urn before the next selection. This is known as sampling with replacement .

An urn contains nred and mblue balls. They are withdrawn one at a time until a total ofr,r...n, red balls have been withdrawn. Find the probability that a total of kballs

are withdrawn.

Hint: A total of kballs will be withdrawn if there are r−1red balls in the first k−1withdrawal and the kth withdrawal is a red ball.

Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck, what is the probability that neither you nor the dealer is dealt a blackjack?

The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a2,3,or12, the player loses; if the sum is either a 7or an 11, the player wins. If the outcome is anything else, the player continues to roll the dice until she rolls either the initial outcome or a 7. If the 7comes first, the player loses, whereas if the initial outcome reoccurs before the 7appears, the player wins. Compute the probability of a player winning at craps.

Hint: Let Eidenote the event that the initial outcome is iand the player wins. The desired probability is ∑i=1212P(Ei). To compute P(Ei), define the events Ei,nto be the event that the initial sum is i and the player wins on the nth roll. Argue that

P(Ei)=∑n=1∞P(Ei,n)

Prove the following relations:

EF⊂E⊂E∪F
See all solutions

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