Question

Patricia was having fun playing poker. She needed the next two cards dealt to be spades so she could make a flush (five cards of the same suit). There are 12 cards left in the deck, and three are spades. What is the probability that the two cards dealt to Patricia (without replacement) will both be spades? Answer choices are in percentage format, rounded to the nearest whole number.

Answer 1

Answer:

4.5% ≈ 5%

Step-by-step explanation:

Given Data :

number of cards left in the deck = 12

number of spades left = 3

Patricia needs 2 spades

Calculate the probability that the two cards dealt ( without replacement ) will both be spades

1st case: ( first card is a spade )

number of cards left in the deck = 12

number of spades left = 3

P( first card dealt is spade ) = 3 / 12 = 1/4

2nd case ( second card is a spade )

number of cards left = 11

number of spades left = 2

p( second card dealt is spade ) = 2/11

Hence the probability that the two cards dealt ( without replacement ) will both be spades

= 1st case * 2nd case

= 1/4 * 2/11

= 2 / 44 =  1 / 22 =  0.045  = 4.5% ≈ 5%