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Math  /  Data & Statistics

QuestionQuestion 2 1 pts
You randomly select one card from a 52-card deck. Find the probability of selecting: an ace or a 9 ? 10 132\frac{13}{2} 513\frac{5}{13} 213\frac{2}{13}

Studdy Solution

STEP 1

1. A standard deck of cards has 52 cards.
2. There are 4 aces and 4 nines in a standard deck.
3. The events of selecting an ace and selecting a 9 are mutually exclusive.

STEP 2

1. Determine the total number of favorable outcomes.
2. Calculate the probability of selecting an ace or a 9.

STEP 3

Determine the number of aces in the deck:
There are 4 aces in a standard deck.

STEP 4

Determine the number of nines in the deck:
There are 4 nines in a standard deck.

STEP 5

Calculate the total number of favorable outcomes for selecting an ace or a 9:
4 (aces)+4 (nines)=8 4 \text{ (aces)} + 4 \text{ (nines)} = 8

STEP 6

Calculate the probability of selecting an ace or a 9:
The probability is given by the ratio of favorable outcomes to the total number of cards in the deck:
852 \frac{8}{52}

STEP 7

Simplify the probability:
852=213 \frac{8}{52} = \frac{2}{13}
The probability of selecting an ace or a 9 is:
213 \boxed{\frac{2}{13}}

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