Probability of finding the card?

#1
You get shown 5 cards, which are then shuffled and placed on the table face down. The person who shuffled the cards then asks you to find a specific one. You get 3 tries with no reshuffling in betweeen.

What are the chances of finding the named card?

I simply thought it must be 1/5 + 1/4 + 1/3 (78.3%). Giving it a bit more reflection I don't think it's that simple right?

I was suggested it would be 1/5 + (4/5 * 1/4) + (3/5 * 1/3), 60%

Is the 60% correct? It doesn't make sence to me...

Could someone explain the thought process behind solving this problem?

Cheers
 

BGM

TS Contributor
#2
why \( \frac {3} {5} = 60\% \) makes no sense to you?

You are given 3 cards out of 5. You are not necessary to think that you are taking the 3 cards 1 by 1 - you may just think that you are taking them at once.

Using hypergeometric pmf can also help you to find the probability of the named card is included in the 3 card sample:

\( \frac {\displaystyle \binom {1} {1} \binom {4} {2}} {\displaystyle \binom {5} {3}} \)