Identifying Variables and Relationships - High School Math

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Question

In a standard deck of cards, with replacement, what is the probability of drawing two Ace of Hearts?

Answer

Probability of drawing first ace of hearts: $\frac{1}{52}$

Probability of drawing second ace of hearts: $\frac{1}{52}$

Multiply both probabilities by each other:

$\frac{1}{52}*\frac{1}{52}=\frac{1}{2704}$

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Question

In a standard deck of cards, without replacement, what is the probability of drawing three kings?

Answer

Start with 52 cards, probability of drawing first king: $\frac{4}{52}$

Now you have 51 cards. Probability of drawing second king: $\frac{3}{51}$

Now you have 50 cards. Probability of drawing third king: $\frac{2}{50}$

Multiply all probabilities:

$\frac{4}{52}\frac{3}{51}\frac{2}{50}=\frac{24}{132,600}=\frac{1}{5525}$

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Question

Using a standard deck of cards, what is the probability of choosing a single face card?

Answer

There are cards in a standard deck: cards in suits. There are face cards (King, Queen, Jack) in each suit, so there are total face cards.

Thus the probability of choosing a single face card is $\frac{12}{52}$ or $\frac{3}{13}$ .

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Question

With a standard deck of cards, what is the probability of picking a spade then a red card if there is no replacement?

Answer

In a standard deck of cards:

$P(spade)\cdot P(red)=\frac{13}{52}\cdot \frac{26}{51}=\frac{13}{102}$

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