Andrea ran 4 3/8 miles on

(HMMT Combo 2009) Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expe

myrzilka [38]

The expected number of cards from the card deck that will be strictly between the two jokers is $\frac{52}{3}$ .

The most popular deck of cards used today is a normal 52-card deck of French-suited playing cards. [a] It is the only standard pack[b] used for playing cards in English-speaking nations; but, in many other nations throughout the world, it is used alongside other traditional, frequently older, standard packs with various suit systems, like those with German-, Italian-, Spanish-, or Swiss suits. The English pattern pack is the only one widely accessible in Britain and America and the most popular pattern of French-suited cards globally. The Belgian-Genoese pattern, which was created in France but is also used widely in Spain, Italy, the Ottoman Empire, the Balkans, and much of North Africa and the Middle East, is the second most popular.

Let all pairs of the positions (m,n) of the jokers are equally likely

$P[0]=P[|m-n|=1]=\frac{53}{\left(\begin{array}{c}54 \\2\end{array}\right)}=\frac{2}{27}$

$P[1]=P[|m-n|=2]=\frac{52}{\left(\begin{array}{c}54 \\2\end{array}\right)}=\frac{104}{1431}$

$P[k]=P|m-n|=k+1=\frac{54-k-1}{\left(\begin{array}{c}54 \\2\end{array}\right)}$

the expected value will be

$\begin{array}{l}\sum_{k=1}^{52} \frac{54-k-1}{\left(\begin{array}{c}54 \\2\end{array}\right)} k \\=\frac{1}{1431}\left(\sum_{k=1}^{52} 53 k-k^{2}\right) \\=\frac{1}{1431}\left(\frac{53}{2}(52)(53)-\frac{1}{6}(52)(53)(105)\right)\\=\frac{52}{3}\end{array}$

Therefore, the expected number of cards that will be strictly between the two jokers is $\frac{52}{3}$ .

To learn more about card deck from the given link:

brainly.com/question/13477028

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5 0

2 years ago

For the following, indicate whether a confidence interval for a proportion or mean should be constructed to estimate the variab

Mrrafil [7]

Answer:

Step-by-step explanation:

The research question is given as "Does chewing your food for a longer period of time reduce one's caloric intake of food atdinner?"

Here interest of study variable is "reduction of caloric intake of food at dinner".

For construction of confidence interval, the researcher records the calorie consumption at dinner.

Since calorie consumption is a variable, we need to construct confidence interval for mean.

So correct choice of sentences as "The confidence interval for a mean should be constructed because the variable of interest is an individual's reduction in caloric intake, which is a quantitative variable."

3 0

3 years ago

Graph y = - 3x + 7 .

lbvjy [14]

Answer:

put your first point at 7 in y axis that point go down 3 to the rights side 1 and your point should be at (1,4) then connect the dots and that's how you graph it

Step-by-step explanation:

5 0

3 years ago

Choose the diagram that show's the graph of the inequality 12 ≤ x + 14

andrezito [222]

I’m pretty sure the answer would be B

8 0

3 years ago

Read 2 more answers

A simple random sample of 100 men is chosen form a population with mean height 71 in and standard deviation 2.5 in. What is the

ankoles [38]

Answer:

2.28%

Step-by-step explanation:

The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:

$z=\frac{x-\mu}{\sigma}\\ \\\mu = mean, \sigma=standard\ deviation,x=raw\ score\\\\For\ a\ sample\ n\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\For\ x$

5 0

4 years ago