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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?

a. 13%
b. 29%
c. 33%
d. 10%

Sagot :

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Answer:

d. 10%

Step-by-step explanation:

1. Information to know

15 cards left in the deck, and 5 are diamond, to find the probability of the next 2 cards being diamond, one has to find the probability of the 1st card as a diamond, and then multiply it by the probability of the 2nd card being a diamond.

Remember, probability is;

[tex]\frac{favorable-outcomes}{total-outcomes}[/tex]

2. Find probability 1

favorable out comes; diamond = 5

total outcomes; total cards = 15

probability is; [tex]\frac{5}{15}[/tex]

Simplified; [tex]\frac{1}{3}[/tex]

3. Finding probability 2

If the last card drawn was a diamond then the new numbers will be

favorable outcomes; 4

total outcomes; 14

Probability is; [tex]\frac{4}{14}[/tex]

Simplified; [tex]\frac{2}{7}[/tex]

4. Total probability

Now, one has to multiply the first probability by the second probability to find the probability of the event;

[tex]\frac{1}{3} * \frac{2}{7}[/tex]

= [tex]\frac{2}{21}[/tex]

= 0.095238

~10%

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