To determine the probability of drawing two aces consecutively without replacement, we can multiply the probabilities of each individual draw.
When drawing cards without replacement, the total number of cards in the deck decreases with each draw. A standard deck contains 52 cards, which includes 4 aces.
First, we calculate the probability of drawing an ace on the first attempt. Since there are 4 aces in a deck of 52 cards, the probability is given by:
P(first ace)=524=131.Next, if you successfully draw an ace, there will be 51 cards remaining in the deck, along with 3 aces still available. The probability of drawing a second ace at this point is:
P(second ace∣first ace)=513=171.To find the overall probability of both events occurring—drawing an ace first and then drawing a second ace—we multiply the probabilities of the two individual events:
P(two aces)=P(first ace)×P(second ace∣first ace)=524×513.Carrying out this multiplication, we have:
P(two aces)=524×513=131×171=2211.Therefore, the probability of drawing two aces in succession without replacement is
2211. 100% |  Global |  97% | |
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100% |
|---|
Professional Tutors |
| All of our elite tutors are full-time professionals, with at least five years of tuition experience and over 5000 accrued teaching hours in their subject. |
Global |
International Tuition |
| Based in Cambridge, with operations spanning the globe, we can provide our services to support your family anywhere. |
97% |
Independent School Entrance Success |
| Our families consistently gain offers from at least one of their target schools, including Eton, Harrow, Wellington and Wycombe Abbey. |
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