What is the probability that a five-card poker hand contains a royal flush, that is, the 10, jack, queen, king, and ace of one suit?

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 =

Hence P(Royal Flush) = 4 /  

= 0.00000154 or 0.154 x 10^-6

1

step-by-step explanation:

it's the only multiple of both and the least

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.