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You draw one card from a 52 card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing an eight the first time and a diamond the second time.

Solution

Solution

\frac{1}{52}

Solution steps

Find the probability of drawing an 8 the first time:

\frac{1}{13}

Find the probability of a diamond the second time:

\frac{1}{4}

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

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

= \frac{1}{52}

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You draw one card from a​ 52 card deck. Then the card is replaced in the deck and the deck is​ shuffled, and you draw again. Find the probability of drawing an eight the first time and a diamond the second time.

Solution

Solution

Popular Examples

You draw one card from a 52 card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing an eight the first time and a diamond the second time.