Find the Ace!

Probability Level 3

You have 10 cards in a random order, one of which is an Ace.

You flip them over one at a time into a face up pile, and at some point you must try to predict that the next card you flip over is an Ace.

Clearly one strategy would be to simply predict that the first card you flip over will be an Ace, which gives you a 1 10 \frac{1}{10} chance of predicting the Ace correctly. However, is there a strategy that gives you better odds?

No Yes

Geoff Pilling by Geoff Pilling , 53, USA

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2 solutions

Geoff Pilling
Nov 1, 2018

There are 10 possible strategies, each of which is effectively choosing right at the beginning which of the 10 cards is an Ace, and each has a 1 10 \frac{1}{10} chance of being right.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Parth Sankhe
Nov 1, 2018

You could predict which card you flip over will be an ace.

P( 1 s t 1^{st} )= 1 10 \frac {1}{10}

P( 2 n d ) 2^{nd}) = 9 10 ⋅ 1 9 = 1 10 \frac {9}{10}\cdot\frac {1}{9}=\frac {1}{10} .

This tells us that the probability of correctly predicting an ace on any card is the same = 0.1

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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