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a hand of 13 cards is dealt at random from a bridge deck of 52 cards. find the probability that the hand contains 4 queens. (round your answer to four decimal places.)

Sagot :

The probability of the hand containing 4 queens when picked at random is 0.0026.

We can solve the given question easily using probability,  permutations, and combinations.

 We can pick any card other than the queen in the following number of ways = ⁴⁸C₉  (i)

The queen card can be picked in the following number of ways

= ⁴C₄= 1 (ii)

The total number of ways to choose 13 cards is = ⁵²C₁₃  (iii)

Using the values of (i), (ii), and (iii), we get -

Probability = (⁴⁸C₉ * 1) /  ⁵²C₁₃

= [tex]\frac{48!/9!(48-9)! *1 }{52!/13!(52-13)! }[/tex]

= 1677106640 * 1 / 635013559600

= 0.00264

If this is rounded to four decimal places, we get = 0.0026.

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