Question

one card is drawn from a standard 52-card deck. determine the probability that the card drawn is not a 4.

p(not a 4) =
(simplify your answer.)

Explanation:

Identify the total outcomes and favorable outcomes

We analyze a standard deck of 52 cards.
Let \(S\) be the sample space of drawing one card.
The total number of outcomes is:

$$ n(S) = 52 $$

Let \(A\) be the event that the card drawn is a 4.
Since there are four 4s in a standard deck (one of each suit):

$$ n(A) = 4 $$

Calculate the probability of drawing a 4

Using the definition of theoretical probability:

$$ P(A) = \frac{n(A)}{n(S)} = \frac{4}{52} $$

Apply complementary probability

Using the Complementary Events knowledge point

$$ P(\text{not a 4}) = P(A') = 1 - P(A) = 1 - \frac{4}{52} = \frac{48}{52} $$

Simplify the resulting fraction

Using the Fraction Simplification knowledge point

$$ P(\text{not a 4}) = \frac{48 \div 4}{52 \div 4} = \frac{12}{13} $$

Answer:

One card is drawn from a standard 52-card deck. Determine the probability that the card drawn is not a 4.

\(P(\text{not a 4}) =\) <blank>\(\frac{12}{13}\)</blank>
(Simplify your answer.)