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There are 52 cards in a deck with 13 cards of each of the four suits. Marlin draws one card, put its back and draws another one.What is the probability that she draws a hearts card and then a 6? Enter your answer as a fraction or a decimal rounded to the nearest hundredth.

Solution

Solution

\frac{1}{52}

Solution steps

Find the probability of she draws a hearts card:

\frac{1}{4}

Find the probability of then a 6:

\frac{1}{13}

Since the events are independent, Use the formula

P (X_{1} \land X_{2} \land \dots \land X_{k}) = P (X_{1}) \cdot P (X_{2}) \cdot \dots \cdot P (X_{k})

= \frac{1}{4} \cdot \frac{1}{13}

\frac{1}{4} \cdot \frac{1}{13} = \frac{1}{52}

= \frac{1}{52}

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