Index notation simplify 4^9 x 4^3
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Answer:
There is 1.98% of probability of being dealt a flush in 5-card Poker
Step-by-step explanation:
To know the probability of a flush being dealt, we can calculate the number of cases when that happens and divide it by the total number of cases of poker hands that exist, naming A the event of a flush.
We will use combinations (nCr button on a calculator) to count the number of cases, because we don't care about the order (it is the same to be dealt a 2, 4, 6, 7 and 8 of hearts than the opposite order), being a flush the event when we take 5 cards out of 13 of the same suit, times 1 out of 4 possible suits and the total number of cases is taking 5 random cards out of 52.
That means there is about a 2% of probability of being dealt a flush.
In other words, of every 16660 plays, 33 will be, on average, a flush