Question

Probability question

Answer 1

\(\large \color{black}{\begin{align}& \normalsize \text{Find the probability that when a hand of 7 cards is drawn from a well}\hspace{.33em}\\~\\
& \normalsize \text{shuffled deck of 52 cards, it contains atleast 3 Kings.}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

Total number of possible hands = 52C7

Answer 3

How many kings are there in a full deck ?

Answer 4

4

Answer 5

break the "good" hands into the problem of choosing 4 "not kings" and 3 kings
plus prob of choosing 3 not kings, and 4 kings

Answer 6

what u mean ?

Answer 7

how many ways can you choose 4 "not kings" from the deck?

Answer 8

48

Answer 9

48C4

Answer 10

yes

Answer 11

that gives you all the "4 card" hands with no kings
now pick 3 kings from the king pile (4 cards)
4C3
multiply to get the number of hands with exactly 3 kings

Answer 12

next, we want the number of hands with 4 kings

Answer 13

4C3\(\times \)48C4

Answer 14

4C4×48C3

Answer 15

ok, now add
that is the numerator (# of hands that match our criteria)
as you know the denominator is 52C7

Answer 16

=\(\dfrac{4C4×48C3+4C3×48C4}{52C7}\)

Answer 17

yes

Answer 18

thnks

Answer 19

yw

Answer 20

Thank you very much @phi . I am always in trouble with probability. Your method is PERFECT. It is easy to understand what is going on. Thanks you so much.