# Draw two aces in a row: visual puzzle and solution | SwaVid

From a standard 52-card deck, what is the probability of drawing two aces without replacement? See the complete step-by-step solution.

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Source: https://www.swavid.com/puzzles/two-aces

# Draw two aces in a row

## 1/221, about 0.45%.

### First draw

### Second draw from the changed deck

### Multiply the two chances

SwaVid visual puzzle

From a standard 52-card deck, what is the probability of drawing two aces without replacement?

Detailed solution

Without replacement, the second draw happens from a smaller deck with one fewer ace.

Four of the 52 cards are aces.

One ace is gone and so is one card, leaving 3 aces in 51 cards.

Both events must happen, so multiply.

Using 4/52 twice assumes the first ace went back into the deck. Without replacement the deck shrinks to 51 cards and 3 aces.

- 1 First draw Four of the 52 cards are aces. P(first ace) = 4/52 = 1/13
- 2 Second draw from the changed deck One ace is gone and so is one card, leaving 3 aces in 51 cards. P(second ace) = 3/51 = 1/17
- 3 Multiply the two chances Both events must happen, so multiply. 1/13 × 1/17 = 1/221

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