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compound events
question id : 419299
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you draw two cards from a standard deck of 52 cards. what is the probability of drawing a club and then a diamond consecutively from the deck without replacement?
a $\frac{13}{51}$
b $\frac{13}{105}$
c $\frac{13}{204}$
d $\frac{13}{408}$

Explanation:

Step1: Probability of first card (club)

A standard deck has 13 clubs out of 52 cards.
$\text{Probability (club)} = \frac{13}{52} = \frac{1}{4}$

Step2: Probability of second card (diamond, no replacement)

After drawing one card, 51 cards remain. There are 13 diamonds.
$\text{Probability (diamond)} = \frac{13}{51}$

Step3: Multiply the two probabilities

For consecutive independent (without replacement) events, multiply individual probabilities.
$\text{Total Probability} = \frac{1}{4} \times \frac{13}{51} = \frac{13}{204}$

Answer:

C. $\frac{13}{204}$