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You pick a card at random. $\newline$ $345$ $\newline$ What is $P(4 \text{ or odd})$ ? $\newline$ Write your answer as a fraction or whole number. $\newline$ $\_\_\_\_\_$

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Probability of mutually exclusive events and overlapping events

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Q. You pick a card at random.

\newline

345

\newline

What is

P(4 \text{ or odd})

?

\newline

Write your answer as a fraction or whole number.

\newline

\_\_\_\_\_

Identify total number of cards: Identify the total number of cards and the specific cards of interest. $\newline$ There are $52$ cards in a standard deck. The cards that are $4$ s are: $4$ of hearts, $4$ of diamonds, $4$ of clubs, and $4$ of spades, making $4$ cards. Odd numbered cards are the aces ( $1$ s), $3$ s, $5$ s, $4$ $0$ s, and $4$ $1$ s in each suit, which totals $4$ $2$ cards.
Calculate favorable outcomes: Calculate the total number of favorable outcomes. $\newline$ Since the $4$ s are also part of the odd cards (specifically the $4$ of hearts and $4$ of diamonds), we need to avoid double-counting. There are $2$ odd $4$ s and $2$ even $4$ s, adding $2$ more odd cards to the $20$ already counted gives $22$ favorable outcomes.

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