Expected value of the highest card

MediumProbability Expected Value~8m

You draw four cards from a shuffled standard $52$ -card deck. Card values are Ace $= 1$ , $2$ – $10$ face value, Jack $= 11$ , Queen $= 12$ , King $= 13$ . What is the expected value of the highest card drawn? (Round to the nearest hundredth.)

Show hints (2)+

$E[\max]=\sum_{v\ge1}\mathbb{P}[\max\ge v]$ , with $\mathbb{P}[\max\le v]=\binom{4v}{4}/\binom{52}{4}$ .
There are $4$ cards per value; sum the tail probabilities for $v=1..13$ .

Answer

Reveal answer →

10.95 (± 0.02)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise free Unlock solutions

Asked at: Optiver, SIG

Expected value of the highest card

Answer

Related questions