What is the probability of picking an Ace or a 7 from a standard deck of cards? Write as a simplified fraction.

Answer 1

The probability of an event occurring is equal to the number of ways it can happen divided by the number of things that could happen. In a deck of cards there are 52 possible cards that can be drawn and you've selected 2 (Ace and 7). Since there are 4 of each of these cards in a deck, the number of ways you could draw either value is the number of that cards you're interested in times the number of times each of those cards occurs in the deck divided by the number of cards in the deck. I will simplify this below mathematically.

Probability = (Number of ways an event can occur) / (Number of possible events)

Probability of drawing Ace or 7 = (Number of Aces and 7s in the deck) / (Number of cards)

Number of Aces in a deck = 4

Number of 7s in a deck = 4

Number of cards in a deck = 52

Probability of A or 7 = (4 Aces + 4 Sevens) / 52 cards

8 cards / 52 cards

This simplifies to 2/13 or 15.38%

A simpler way to solve this, specific to a deck of cards, is that there are 13 cards in a suit so the odds of getting any specific card within a suit is 1/13. Since the number of a given card in a deck and the number of suits in a deck increase at the same rate, this simplification can be applied for any value of a suit in a single deck