Question

Annika was having fun playing poker. She needed the next two cards dealt to be diamonds...

Annika was having fun playing poker. She needed the next two cards dealt to be diamonds so she could make a flush (five cards of the same suit). There are 15 cards left in the deck, and five are diamonds.

What is the probability that the two cards dealt to Annika (without replacement) will both be diamonds? Answer choices are in percentage format, rounded to the nearest whole number.

  • 13%

  • 29%

  • 33%

  • 10%

Homework Answers

Answer #1

15 cards left

2 cards are dealt

need 2 diamonds

Case 1: first card is diamond

number of cards = 15

number of diamond cards = 5

P(first card is diamond) = n(diamond cards)/n(total cards)

P(first card is diamond) = 5/15 = 1/3

Case 2: second card is diamond

number of cards = 14

number of diamond cards = 4

P(first card is diamond) = n(diamond cards)/n(total cards)

P(first card is diamond) = 4/14 = 2/7

Final probability = P(Case 1) * P(Case 2)

Final probability = 1/3 * 2/7 = 2/21 = 0.0952

probability that the two cards dealt to Annika (without replacement) will both be diamonds = 9.52% = 10%

Option D is correct

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