Question

A standard deck of 52 cards contains four suits: clubs, spades, hearts, and diamonds. Each deck contains an equal number of cards in each suit. Rochelle chooses a card from the deck, records the suit, and replaces the card. Her results are shown in the table.

Clubs 29, Spades 13, Hearts 15, Diamonds 23

How does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart?
The theoretical probability of choosing a heart is 1\16 greater than the experimental probability of choosing a heart.
The experimental probability of choosing a heart is 1\16 greater than the theoretical probability of choosing a heart.
The theoretical probability of choosing a heart is 1\26 greater than the experimental probability of choosing a heart.
The experimental probability of choosing a heart is 1\26 greater than the theoretical probability of choosing a heart.

Answer 1

Answer:There are 52 cards in a deck in total. Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades). There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total)

Step-by-step explanation:

There are 52 cards in a deck in total. Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades). There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total)

Answer 2

The theoretical probability of choosing a heart is 1\16 greater than the experimental probability of choosing a heart.

Explanation:

We know that the total number of cards in a deck = 52

Total number of hearts = 13

Then the theoretical probability of getting a heart = $\dfrac{\text{Number of cards have hearts}}{\text{Total cards}}=\dfrac{13}{52}=\dfrac{1}{4}=0.25$

Cards chosen by Rochelle : Clubs 29, Spades 13, Hearts 15, Diamonds 23

Total cards  = 80

The experimental probability of getting a heart = $\dfrac{\text{Number of cards have hearts}}{\text{Total cards}}=\dfrac{15}{80}=\dfrac{3}{16}=0.1875$

Since , 0.25 > 0.1875 i.e. Theoretical probability > Experimental probability

And , $0.25-0.1875=0.0625=\dfrac{625}{10000}=\mathbf{\dfrac{1}{16}}$

Hence , the theoretical probability of choosing a heart is 1\16 greater than the experimental probability of choosing a heart.

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