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Katy chose a card at random from a deck of 52 cards. Katy replaced the first card and then chose a second card. What is the probability that Katy chose a diamond both times?

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There are 13 cards in the suit of diamonds. The probability of randomly choosing a diamond is 13/52 = 1/4. The two events 'draw a diamond' are independent, therefore the probability of drawing a diamond both times is:
[tex]P(diamond\ both\ times)=\frac{1}{4}\times\frac{1}{4}=?[/tex]

Answer: Our required probability is [tex]\dfrac{1}{16}[/tex]

Step-by-step explanation:

Since we have given that

Number of cards in deck = 52

Number of diamond in a deck = 13

So, Probability of getting diamond in first time = [tex]\dfrac{13}{52}=\dfrac{1}{4}[/tex]

she replaced the first card, then chose a second card.

So, probability of getting diamond second time = [tex]\dfrac{13}{52}=\dfrac{1}{4}[/tex]

So, Probability that she chose a diamond both times is given by

[tex]\dfrac{1}{4}\times \dfrac{1}{4}\\\\=\dfrac{1}{16}[/tex]

Hence, our required probability is [tex]\dfrac{1}{16}[/tex]

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