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anyanavicka [17]
3 years ago
5

g What is the probability of being dealt exactly three of a kind (like three kings or three 7’s, etc.) in a five card hand from

a deck of 52 cards?
Mathematics
1 answer:
Elena L [17]3 years ago
8 0

Answer: 0.02257

Step-by-step explanation:

Given : Total cards in a deck = 52

Number of ways to select any 5 cards : ^{52}C_5

Since , there are total 13 kinds of card (includes Numbers from 2 to 9 and Ace , king, queen and jack).

Of each kind , there are 4 cards.

Number of ways to select three cards in a five card hand of a single kind : ^{4}C_3\times^{48}C_2

Number of ways to select three cards in a five card hand of a exactly three of a kind : 13\times^{4}C_3\times^{48}C_2

Now , the required probability = \dfrac{13\times^{4}C_3\times^{48}C_2}{^{52}C_5}

=\dfrac{13\times4\times\dfrac{48!}{2!46!}}{\dfrac{52!}{5!47!}}\\\\\\=\dfrac{58656}{2598960}

=0.022569027611\approx0.02257

∴ The probability of being dealt exactly three of a kind (like three kings or three 7’s, etc.) in a five card hand from a deck of 52 cards= 0.02257

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