Multiple choice

There are n cards in a pack numbered from 1 to n. A and B are two individuals who draw a card from the pack. Find the probability that the card drawn by A is higher than that drawn by B. A

  1. $\dfrac1n$
  2. $\dfrac{n-1}{2n}$
  3. $\dfrac{n+1}{2n}$
  4. $\dfrac{n-1}{n}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are n(n - 1) ordered outcomes in which the two cards are different. Exactly half of these have A's card higher than B's, so favorable outcomes equal n(n - 1)/2. The probability is therefore (n - 1)/(2n).

AI explanation

When drawing two cards, there are n times (n-1) total possible outcomes where A draws first and B draws second without replacement. For A to draw a higher card than B, if A draws the number x, there are exactly (x - 1) cards lower than it for B to draw, giving a total of the sum of integers from 1 to (n-1) favorable outcomes. This sum is calculated as (n-1)n / 2, making the probability [(n-1)n / 2] divided by [n(n-1)]. This simplifies to (n - 1) / (2n).

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