A probability problem by Achal Jain

Probability Level pending

In shuffling a pack of playing cards, four cards were accidentally dropped. Find the probability that the missing cards should be one from each suit.

Give your answer to 3 decimal places.


The answer is 0.105.

Achal Jain by Achal Jain , 19, India

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1 solution

Paul Hindess
Jan 1, 2017

The first card could be any of the 52 cards.

The second can only be one of the 39 in the remaining 3 suits.

The third card can only be one of the 26 in the remaining 2 suits.

The fourth card can only be one of the 13 in the only remaining suit.

The number of cards we have to choose from is decreasing by 1 with every card we pick, so we have the answer:

52 52 × 39 51 × 26 50 × 13 49 = 0.105 \frac{52}{52}\times\frac{39}{51}\times\frac{26}{50}\times\frac{13}{49}=0.105 to 3 decimal places.

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