Answered: Consider a deck of cards. Suppose we…

Name: Consider a deck of cards. Suppose we are drawing ten cards with replac
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Description: Consider a deck of cards. Suppose we are drawing ten cards with replacement. What is the probabilityof finding at least 4 face cards?

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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Consider a deck of cards. Suppose we are drawing ten cards with replacement. What is the probabilityof finding at least 4 face cards?

Expert Solution

Step 1

A deck of cards contains 52 cards. 12 cards are face cards.

Since 10 cards are drawn with replacement, then the probability of selecting a card every time is equal.

The probability of selecting a face card is

$= \frac{Total number of ways a face card is drawn}{Total number of ways a card is drawn} = \frac{(\begin{matrix} 12 \\ 1 \end{matrix})}{(\begin{matrix} 52 \\ 1 \end{matrix})} = \frac{12}{52}$

Suppose, X be the number of face cards drawn out of 10 draws.

Then X follows Binomial distribution with parametres $n = 10, p = \frac{12}{52} .$

Hence, the probability mass function is

$P [X = x] = (\begin{matrix} 10 \\ x \end{matrix}) {(\frac{12}{52})}^{x} {(1 - \frac{12}{52})}^{(10 - x)}, x = 0, 1, 2 . . 10 . = (\begin{matrix} 10 \\ x \end{matrix}) {(\frac{12}{52})}^{x} {(\frac{40}{52})}^{(10 - x)}, x = 0, 1, 2 . . . . 10 .$

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