Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A pack contains m cards, labeled 1, 2,....,m. The cards are dealt out in a random order, one by one. Given that the label of the kth card dealt is the largest of the first k cards, what is the probability that it is also the largest in the whole pack?

Reading probability myself and stuck at some questions.

share|improve this question

2 Answers 2

(You might want this to get double-checked by someone else; my probability is a bit rusty.)

Recall the formula for conditional probability: $$ \begin{align} P(A \cap B) &= P(A|B)P(B) \\ P(A|B) &= \frac{P(A \cap B)}{P(B)} \end{align}$$

Here, let $A$ be the event that the $k$th card is the largest of the $m$ cards, and $B$ be the event that the $k$th card is the largest of the $k$ cards drawn.

Since $A$ implies $B$, $P(A \cap B) = P(A)$. So the probability is $1/m$. The probability of event $B$, that the $k$th card is the largest of $k$ cards, without knowing any other information, is $1/k$.

Then $$P(A|B) = \frac{1/m}{1/k} = \frac{k}{m}.$$

share|improve this answer

The probability is equal to the probability that the largest of m cards is one of the first k cards, which is $\frac{k}{m}$.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.