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jasenka
16 days ago
10

This question refers to a standard deck of playing cards. If you are unfamiliar with playing cards, there is an explanation in P

robability of an event' section under the heading Standard playing cards. A five-card hand is just a subset of 5 cards from a deck of 52 cards. How many different five-card hands are there from a standard deck of 52 playing cards? How many five-card hands have exactly two hearts? How many five-card hands are made entirely of hearts and diamonds? How many five-card hands have four cards of the same rank? A full house" is a five-card hand that has two cards of the same rank and three cards of the same rank. For example, (queen of hearts, queen of spades, 8 of diamonds, 8 of spades, 8 of clubs). How many five-card hands contain a full house? How many five-card hands do not have any two cards of the same rank?
Computers and Technology
2 answers:
Amiraneli [921]16 days ago
5 0

Answer:

The total number of combinations is 2595960

P(two hearts) = 0.003 %

P(hearts and diamonds) = 63.73 %

P(4 same rank) = 0.024 %

P(full house) = 0.144 %

P(No same rank) = 50.7 %

Explanation:

How many unique five-card hands can be created from a standard deck of 52 cards?

There are 52 cards to choose from, and we need to pick 5 cards

The number of combinations equals 52C5

The total combinations = 2595960

Now, how many five-card hands contain precisely two hearts?

We have 13 hearts, and we need to select two of them

P(two hearts) = 13C2/52C5

Resulting in: P(two hearts) = 78/2598960

So, P(two hearts) = 0.003 %

What about five-card hands composed solely of hearts and diamonds?

P(hearts and diamonds) = 13C5*13C5/52C5

P(hearts and diamonds) = 1287*1287/2598960

Thus, P(hearts and diamonds) = 1656369/2598960

This gives P(hearts and diamonds) = 63.73 %

How many five-card hands have four cards of the same rank?

P(4 same rank) = 13C1*12C1*4C1/5C2

So we have P(4 same rank) = 13*12*4/2598960

Consequently, P(4 same rank) = 624/2598960

Resulting in P(4 same rank) = 0.024 %

For five-card hands containing a full house, we have

P(full house) = 13C2*2C1*4C3*4C2/5C2

This results in P(full house) = 78*2*4*6/2598960

Thus P(full house) = 3744/2598960

Giving us P(full house) = 0.144 %

Finally, how many hands have no two cards of the same rank?

P(No same rank) = 13C5*4C1*4C1*4C1*4C1*4C1/5C2

Calculating gives P(No same rank) = 1287*4*4*4*4*4/2598960

Hence P(No same rank) = 1317888/2598960

Leading to P(No same rank) = 50.7 %

Amiraneli [921]16 days ago
4 0

Answer:

Explanation:

The number of combinations to select 10 girls is 35C₁₀

The number of combinations to select 10 boys is also 35C₁₀

Thus, the total combinations for selection is 35C₁₀ x 35C₁₀

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Harlamova29_29 [932]

Answer:

#SECTION 1

while True:

   month = input("Input the month (e.g. January, February etc.): ")

   try:

       

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           day = int(input("Input the day: "))

           try:

               if day > 31:

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               elif day == 31 and month in ('September', 'April', 'June', 'November'):

                   raise

               elif day > 29 and month == 'February':

                   raise

               else:

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           except:

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       else:

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   except:

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#SECTION 2

if month in ('January', 'February', 'March'):

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elif month in ('April', 'May', 'June'):

season = 'spring'

elif month in ('July', 'August', 'September'):

season = 'summer'

else:

season = 'autumn'

if (month == 'March') and (day > 19):

season = 'spring'

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season = 'summer'

elif (month == 'September') and (day > 21):

season = 'autumn'

elif (month == 'December') and (day > 20):

season = 'winter'

print("Season is", season)

Explanation:

#SECTION 1

This section is designed to ensure that the user inputs a valid month and day. The try and except blocks paired with IF statements work together to achieve accurate results. The while loop continues until a legitimate input is received.

The first try block checks if the month provided exists by comparing it against a predefined list. If it fails, an error is raised, triggering the except block that informs the user of the invalid entry.

When the first TRY block succeeds, it moves to the next stage, which takes a number input, confirming that it is correct for each month. Any invalid input leads to an error, stimulating the try block to print the issue.

If all inputs are valid, the program exits the loop and transitions to the subsequent section.

#SECTION 2

This part uses the given data to determine the season, leveraging IF statements to produce the result, which it then prints.

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Answer:

Below is the JAVA program:

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      for (int i = 0; i < frequency.length; i++) {  //iterates through frequency array

          count = 0;  //sets count to zero

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                  count++;                 }            }  //increments count

          frequency[i] = count;      }  //stores count in the frequency array

      for (int i = 0; i < stringArray.length; i++) {  //iterates through the string array

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Explanation:

To illustrate the program, consider:

let integer = 3

for (int i = 0; i < integer; i++) is used to input strings into stringArray.

On the first pass:

i = 0

0<3

stringArray[i] = input.next(); takes a word and saves it to the ith index of stringArray. For example, if the user types "hey", it will be in stringArray[0].

Then, i increments to i = 1

On the second pass:

i = 1

1<3

stringArray[i] = input.next(); takes another word and assigns it to stringArray[1]. If the user enters "hi", then hi will be in stringArray[1]

Next, i becomes i = 2

On the third pass:

i = 2

2<3

stringArray[i] = input.next(); captures a word and places it in stringArray[2]. If the user types "hi", it goes to stringArray[2]

Then, i increments to i = 3

The loop terminates since i<integers is false.

The next outer loop for (int i = 0; i < frequency.length; i++) and inner loop for (int j = 0; j < frequency.length; will check each word and if (stringArray[i].equals(stringArray[j])) identifies any duplicates. Words that repeat will have their count incremented and the frequency array will record these values. For example, hey appears once while hi shows up twice, thus resulting in the final outputs:

hey 1

hi 2

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The visual representation of the program and its outcome based on the example provided is attached.

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Harlamova29_29 [932]

Answer:

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Explanation:

#include <stdio.h>

#include <stdbool.h>

int main(void) {

int userNum;

bool isPositive;

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scanf("%d", &userNum);

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printf("\n");

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In this expression, we observe that the '2' in the hundred's place must be converted to '0' while carrying over '1' to the thousand's position, leading to;

101₂ + 0₂ + 10100₂ = 11001₂.

This shows that;

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Next, we convert the outcome of squaring the base 2 number, 11001₂, into base 10 through the following method;

Converting 11001₂ to base 10 results in;

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