Answer:
0.00000154 or 0.154 x 10^-6
Step-by-step explanation:
P (Royal Flush) = Number of ways to get a Royal Flush / Number of possible 5 card hands
Because there are 4 suits (Spades, Hearts, Clubs, Diamonds), the possible ways to get a royal flush are as follows
1) Spades (10,J,K,Q,A)
2) Hearts (10,J,K,Q,A)
3) Clubs (10,J,K,Q,A)
4) Diamonds (10,J,K,Q,A)
Hence there are 4 ways to get a Royal Flush (i.e numerator)
In order to find the number of 5 card hands, we know that a full deck as 52 cards, and we want to pick 5 cards from the deck of 52 and order does not matter. Hence
Number of possible 5 card hands = [tex]=^{52} C_{5}[/tex]
Hence P(Royal Flush) = 4 / [tex]=^{52} C_{5}[/tex]
= 0.00000154 or 0.154 x 10^-6
The required probability of the five-card poker hand containing a royal flush, that is, the 10, jack, queen, king, and ace of one suit is 0.153E-6.
Given that,
The probability for a five-card poker hand contains a royal flush, that is, the 10, jack, queen, king, and ace of one suit is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
A deck of cards contains 52 card and 5 cards to be randomly selected,
Total number of samples = number of combination
= 52C5
= 2,598,960
Favorable events = {Spades (10 J K Q A ,Hearts (10 J K Q A) Clubs(10 J K Q A), Diamonds (10 J K Q A)}
Number of favorable events = 4
Probability for five-card poker hand containing a royal flush, that is, the 10, jack, queen, king, and ace of one suit,
P = 4 / 2, 598, 960
P = [tex]0.153 * 10^-6[/tex]
Thus, the required probability of the five-card poker hand containing a royal flush, that is, the 10, jack, queen, king, and ace of one suit is 0.153E-6.
Learn more about probability here:
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