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A magician is performing a card trick where he will pick a card you name from a standard deck of cards. What is the probability of the magician selecting the card you name?

A. [tex]\frac{1}{25}[/tex]
B. [tex]\frac{1}{1,000,000}[/tex]
C. [tex]\frac{4}{25}[/tex]
D. [tex]\frac{1}{52}[/tex]

Sagot :

GinnyAnsweridn
Let's address the probability of selecting a specific card from a standard deck of 52 cards.

1. Identify the Total Number of Possible Outcomes:
- A standard deck of cards contains 52 cards.

2. Identify the Number of Favorable Outcomes:
- There is only one card that you name. Thus, the number of favorable outcomes is 1.

3. Calculate the Probability:
- The probability, [tex]\( P \)[/tex], of an event is given by the number of favorable outcomes divided by the total number of possible outcomes.
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \][/tex]
- Substituting the values:
[tex]\[ P = \frac{1}{52} \][/tex]

4. Verification with Options:
- Option A: [tex]\(\frac{1}{25}\)[/tex] is not correct as 25 is not the total number of cards in a standard deck.
- Option B: [tex]\(\frac{1}{1,000,000}\)[/tex] is not correct as 1,000,000 is not the total number of cards in a standard deck.
- Option C: [tex]\(\frac{4}{25}\)[/tex] is incorrect because it simplifies to a probability of 0.16, which does not align with the given probabilities of individual cards in a standard deck.

Therefore, the best answer is:
D. [tex]\(\frac{1}{52}\)[/tex]
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