# How to calculate the chance of drawing 2 copies of 2 different types of cards in a 40 card deck

Discussion in 'Probability and Statistics' started by dancewithchance, Mar 5, 2023.

1. ### dancewithchance

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There are 3 copies of 2 different cards each in the 40 card deck. You draw a hand of 5 cards. How do i calculate the probability of drawing at least 1 copy of the 1st card and 2 copies of the 2nd card in the 5 card hand?

dancewithchance, Mar 5, 2023

2. ### apprentus

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To calculate the chance of drawing 2 copies of 2 different types of cards in a 40 card deck, we can use the following formula:

P = (n1/N) x ((n2-1)/(N-1)) x 2

Where P is the probability of drawing 2 copies of 2 different types of cards, n1 is the number of cards of the first type, n2 is the number of cards of the second type, N is the total number of cards in the deck, and the factor of 2 at the end accounts for the fact that we could draw the cards in either order (i.e., the first card could be of type 1 and the second card of type 2, or vice versa).

Let's assume we have a 40 card deck with 20 cards of type A and 20 cards of type B. Plugging these values into the formula, we get:

P = (20/40) x ((20-1)/(40-1)) x 2 P = 0.5 x (19/39) x 2 P = 0.487

Therefore, the chance of drawing 2 copies of 2 different types of cards in a 40 card deck with 20 cards of each type is approximately 0.487, or about 48.7%.

apprentus, Mar 10, 2023

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