Q. 49 49. Checking independence In whi... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 6: Q. 49 (page 379)

49. Checking independence In which of the following games of chance would you be willing to assume independence of $X$ andlocalid="1649903939419" $Y$ in making a probability model? Explain your answer in each case.
(a) In blackjack, you are dealt two cards and examine the total points localid="1649903945891" $X$ on the cards (face cards count localid="1649903950298" $10$ points). You can choose to be dealt another card and compete based on the total pointslocalid="1649903956461" $Y$ on all three cards.
(b) In craps, the betting is based on successive rolls of two dice. localid="1649903966379" $X$ is the sum of the faces on the first roll, and localid="1649903971075" $Y$ is the sum of the faces on the next roll.

Short Answer

Expert verified

(a) Dependent, because the cards cannot be said to the independent events.

(b) The two events $X$ and $Y$ are independent events.

Step by step solution

Part (a) Step 1: Given information

Given in the question that, In blackjack, are dealt two cards. And then choose to be dealt another card and compete based on the total points $Y$ on all three cards.

Part (a) Step 2: Explanation

Handled two cards in blackjack and studied the all-out focus $X$ on the cards (face cards check ten focuses). And choose another card to be addressed; thus, on each of the three cards, contend based on the all-out direction $Y$ .

Because the second card has been set without replacing the deck with the cards, the events $X$ and $Y$ cannot be assumed to be independent.

Part (b) Step 1: Given information

The betting is based on successive rolls of two dice. $X$ is the sum of the faces on the first roll, and $Y$ is the sum of the faces on the next roll.

Step (b) Step 2: Explanation

Two events $X$ and $Y$ are independent. Because the faces of both rolls do not influence each other, . There is a probability that the exact number will appear on both rolls.