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# Five cards are selected at random without replacement from

ISBN: 9780321923271 41

## Solution for problem 15E Chapter 2.1

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition

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Problem 15E

Five cards are selected at random without replacement from a standard, thoroughly shuffled 52-card deck of playing cards. Let X equal the number of face cards (kings, queens, jacks) in the hand. Forty observations of X yielded the following data:

(a) Argue that the pmf of X is

and thus, that f (0) = 2109/8330, f (1) = 703/1666, f (2) = 209/833, f (3) = 55/833, f (4) = 165/21,658, and f (5) = 33/108,290.

(b) Draw a probability histogram for this distribution.

(c) Determine the relative frequencies of 0, 1, 2, 3, and superimpose the relative frequency histogram on your probability histogram.

Step-by-Step Solution:

Step 1of 3 :

Five cards are selected at random without replacement from a standard,thoroughly shuffled 52-card deck of playing cards.

Let X equal the number of face cards (kings,queens,jacks ) in hand.

a).

There are 12 face cards among 52 cards.We can select the number of number of face cards in any one  ways and 52 cards not face cards in any one ways, by the multiplication principle product is   equals the number of ways the joint operation can he performed .

If we assume that each of ways of selecting 5 objects from 52 objects has the same probability.

Here X = number of face cards.

12 = total number of face cards.

40 = total number of non face cards.

Then,

f(x) =  , x = 0,1,2,3,4,5

So put x = 0,1,2,3,4, and 5

Then,

f(0) =

f(0) = 0.2532

f(1) =

f(1) = 0.42197

f(2) =

f(2) = 0.251

f(3) =

f(3) = 0.066

f(4) =

f(4) = 0.00762  and

f(5) =

f(5) = 0.00030

Step 2 of 3 :

b).

We have drawn a probability for this distribution.

 f(x) h(x) 0 0.2532 0.325 1 0.4219 0.4 2 0.251 0.225 3 0.066 0.05 4 0.0076 0 5 0.0003 0

Then the graph is given below.

Step 3 of 3

##### ISBN: 9780321923271

Since the solution to 15E from 2.1 chapter was answered, more than 298 students have viewed the full step-by-step answer. The answer to “Five cards are selected at random without replacement from a standard, thoroughly shuffled 52-card deck of playing cards. Let X equal the number of face cards (kings, queens, jacks) in the hand. Forty observations of X yielded the following data: (a) Argue that the pmf of X is and thus, that f (0) = 2109/8330, f (1) = 703/1666, f (2) = 209/833, f (3) = 55/833, f (4) = 165/21,658, and f (5) = 33/108,290.(b) Draw a probability histogram for this distribution.(c) Determine the relative frequencies of 0, 1, 2, 3, and superimpose the relative frequency histogram on your probability histogram.” is broken down into a number of easy to follow steps, and 102 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. This full solution covers the following key subjects: Cards, histogram, relative, Probability, Observations. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The full step-by-step solution to problem: 15E from chapter: 2.1 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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