5. Let X be the random variable that represents the number of hearts in a 4 card hand drawn from a standard deck. (a) What is the probability distribution of X?
5. Let X be the random variable that represents the number of hearts in a 4 card hand drawn from a standard deck. (a) What is the probability distribution of X?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:5. Let \( X \) be the random variable that represents the number of hearts in a 4 card hand drawn from a standard deck.
(a) What is the probability distribution of \( X \)?
(b) What is the expected value of \( X \)?
Expert Solution
Step 1
Introduction :
There are 13 hearts and 39 non-heart cards in a deck of 52 cards.
Based on the standard deck, there are four ways to draw four cards from it
The number of hearts and non-hearts cards to be selected is 13Ck 39C4−k.
It is possible to select 4 cards from the deck in 52C4 different ways.
As a result, the probability of getting k hearts is 13Ck 39C4−k / 52C4.
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