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?
please show explanation
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.
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.