A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) through (c) to obtain the probability of being dealt a flush in five cards.

(a) Initially concentrate on one suit, say diamonds. There are 13 diamonds

in a deck. Compute P(five diamonds)=P(first card is diamonds and second card is diamonds

and third card is diamonds and fourth card is diamonds and fifth card is diamonds).

In a standard 52-card deck, P(five

diamonds)=. 000495 (Round to six decimal places as needed.)

(b) A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive.

In a standard 52-card deck, P(five clubs or five diamonds or five hearts or five

spades)=. 002 (Round to three decimal places as needed.)

(c) A royal flush in the game of poker occurs if the player gets the cards Ten, Jack, Queen, King, and Ace all in the same suit. Use the procedure given in parts (a) and(b) to compute the probability of being dealt a royal flush.

In a standard 52-card deck, P(royal

flush)= __?__ (Round to eight decimal places as needed.)