Question

checking your understanding
marco is playing a game with a standard deck of cards. the first person to select a heart from the deck without looking wins.
what is the theoretical probability that marco will choose a card with a heart on it?
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what is the theoretical probability that marco will choose a card without a heart on it?
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Explanation:

First Sub - Question: Probability of choosing a heart

Step1: Determine total number of cards

A standard deck has 52 cards, so total outcomes $n = 52$.

Step2: Determine number of heart cards

There are 13 heart cards in a deck, so favorable outcomes for heart $m = 13$.

Step3: Calculate probability

Probability $P=\frac{m}{n}=\frac{13}{52}=\frac{1}{4}$.

Second Sub - Question: Probability of choosing a non - heart

Step1: Determine total number of cards

A standard deck has 52 cards, so total outcomes $n = 52$.

Step2: Determine number of non - heart cards

Number of non - heart cards $= 52 - 13=39$.

Step3: Calculate probability

Probability $P=\frac{39}{52}=\frac{3}{4}$.

Answer:

$\frac{1}{4}$