Question

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.

O 10%
O 29%
O 33%
O 13%

Answer 1

The probability of Annika getting two diamonds in a row without replacement from 15 cards with 5 diamonds is 33%, after calculating the individual probabilities of each event and then multiplying them together.

option c is the correct

Step-by-step explanation:

The question involves determining the probability that the next two cards Annika is dealt from the remaining deck will both be diamonds. In the deck, there are 15 cards left with 5 being diamonds, and she needs two of them for a flush. The probability of the first card being a diamond is 5 out of 15, or ⅓. If that first card is indeed a diamond, there will be 14 cards left and 4 of them will be diamonds. So, the probability the second card is also a diamond is 4 out of 14, or ⅗.

To find the total probability of both events occurring, we multiply the probabilities of each event:

⅓ * ⅗ = ⅖0, which simplifies to ⅓5. Converting this into a percentage gives us 100 * ⅓5 = 33.33%, which we round to the nearest whole number, resulting in 33%.