Three cards are drawn without replacement from the 16 cards that make up the 10s, jacks, queens, and kings from an ordinary deck of 52 playing cards. Let X be the number of queens selected and Y the number of kings (a) Find the joint probability distribution of X and Y. (b) Find P[(X,Y)EA], where A is the region given by {(x,y) | x + y 2 1). (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) f(x.y) 1 2 3 y 1 2 3 (b) P((X,Y)EA] = (Type an integer or simplified fraction.)
Three cards are drawn without replacement from the 16 cards that make up the 10s, jacks, queens, and kings from an ordinary deck of 52 playing cards. Let X be the number of queens selected and Y the number of kings (a) Find the joint probability distribution of X and Y. (b) Find P[(X,Y)EA], where A is the region given by {(x,y) | x + y 2 1). (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) f(x.y) 1 2 3 y 1 2 3 (b) P((X,Y)EA] = (Type an integer or simplified fraction.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Problem Statement:**
Three cards are drawn without replacement from the 16 cards that make up the 10s, jacks, queens, and kings from an ordinary deck of 52 playing cards. Let \( X \) be the number of queens selected and \( Y \) the number of kings.
**Tasks:**
(a) Find the joint probability distribution of \( X \) and \( Y \).
(b) Find \( P((X, Y) \in A) \), where \( A \) is the region given by \(\{(x, y) \mid x + y \geq 1\}\).
**Instructions for Solving:**
(a) Complete the joint probability distribution table. Use integers or simplified fractions to fill in the table.
**Table:**
| \( f(x, y) \) | 0 | 1 | 2 | 3 |
|--------------|-----|-----|-----|-----|
| y = 0 | | | | |
| y = 1 | | | | |
| y = 2 | | | | |
| y = 3 | | | | |
(b) Calculate \( P((X, Y) \in A) \). Enter the probability as an integer or a simplified fraction.
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