If 5 cards are drawn one after another without replacement from a standard deck of 52 cards, what is the probability of drawing, in sequence, a diamond, a spade, a heart, a club, and another diamond?

Answer Choices

Correct answer marked below

\frac{13}{52}⋅\frac{13}{51}⋅\frac{13}{50}⋅\frac{13}{49}⋅\frac{12}{48}

Correct

\frac{13}{52}⋅\frac{12}{51}⋅\frac{11}{50}⋅\frac{10}{49}⋅\frac{9}{48}

\frac{5}{52}⋅\frac{5}{51}⋅\frac{5}{50}⋅\frac{5}{49}⋅\frac{5}{48}

\frac{13}{52}⋅\frac{13}{52}⋅\frac{13}{52}⋅\frac{13}{52}⋅\frac{13}{52}

\frac{13}{52}⋅\frac{12}{52}⋅\frac{11}{52}⋅\frac{10}{52}⋅\frac{9}{52}

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Explanation

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Official Explanation

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In a standard deck of 52 cards, there are 13 cards of each suit. To find the probability of drawing a diamond first, we have 13 options out of 52 total cards. Thus, the probability of drawing a diamond is

\frac{13}{52}

. After drawing a diamond, we then draw a spade, which also has 13 cards available, but now there are only 51 cards left. Therefore, the probability of…

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Comments

JasleenMar 13, 2024

Greatt

ArvindSep 19, 2024

pls explain more?

What this question tests

What it tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Common trap

Forgetting to use the complement for 'at least one', or treating dependent events as independent.