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Satara was having fun playing poker. She needed the next two cards dealt to be hearts so she could make a flush (five cards of the same suit). There are 10 cards left in the deck, and three are hearts. What is the probability that the two cards dealt to Satara (without replacement) will both be hearts? Answer choices are in percentage format, rounded to the nearest whole number.

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Answer:

7%

Step-by-step explanation:

Given the following :

Total Number of cards left in deck = 10

Number of hearts left in deck = 3

Probability = (required outcome / Total possible outcomes)

Required outcome = hearts card in deck

Two cards are to be dealt to Satara without replacement :

Probability of 1st card being hearts :

P(1st card being hearts) = required outcome / Total possible outcomes

P(1st card being hearts) = 3 / 10

Probability of 2nd card being hearts :

Since it is without replacement :

Required outcome = (3 - 1). = 2

Total possible outcomes = (10 - 1) = 9

P(2nd card being hearts) = 2 /9

Probability of the two cards being hearts :

(3 / 10 × 2/9) = 6 /90 = 0.0666

0.06666 × 100% = 6.66%

= 7% (nearest whole number)

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