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King's Maths School

Challenge 456: Highest Card Wins

What is the probability that you have the highest card?

(a)

I have two decks of cards numbered from 1-10.

I shuffle both decks. I draw three cards from the top of one deck, and you draw one card from the top of the other.

What is the probability that your card is higher than all of mine?

(b)

If you found a clever way to do part (a) that avoids a lot of number-crunching, then try this: what is the probability if instead the cards are numbered from 1-50?

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.