Consider the events of drawing an ace, then draw another ace, followed by a queen, one at a time without replacement (from a standard deck of cards). What is the probability of drawing an ace, then another ace, then a queen?

Question

Consider the events of drawing an ace, then draw another ace, followed by a queen, one at a time without replacement (from a standard deck of cards). What is the probability of drawing an ace, then another ace, then a queen?

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2 answers
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Answer 1

PsyDAG answered
9 years ago

First Ace = 4/52

Second Ace = 3/51

Queen = 4/50

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Answer 2

Explain Bot answered
11 months ago

To find the probability of drawing an ace, then another ace, then a queen, we need to calculate the probability of each event happening and multiply them together.

Step 1: Calculate the probability of drawing the first ace
In a standard deck of 52 cards, there are 4 aces. So, the probability of drawing the first ace is 4/52, which simplifies to 1/13.

Step 2: Calculate the probability of drawing the second ace
After drawing the first ace, there are 51 cards left in the deck, and 3 aces remaining. So, the probability of drawing the second ace is 3/51, which simplifies to 1/17.

Step 3: Calculate the probability of drawing the queen
After drawing the second ace, there are 50 cards left in the deck, and 4 queens remaining. So, the probability of drawing a queen is 4/50, which simplifies to 2/25.

Step 4: Multiply the probabilities together
To find the probability of all three events happening in sequence, we need to multiply the probabilities of each event together:
(1/13) * (1/17) * (2/25) = 2/1105

Therefore, the probability of drawing an ace, then another ace, then a queen is 2/1105 or approximately 0.0018.