A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two flowers are randomly selected without replacement. What is the probability of selecting two carnations? Express the answer in the simplest form of fraction.
There are 18 flowers in total, so the probability of selecting one carnation on the first pick is 6/18. After one carnation is picked, there are 17 flowers remaining, including 5 begonias and 6 carnations. So the probability of picking another carnation on the second pick, given that the first pick was a carnation, is 5/17.
Therefore, the probability of selecting two carnations is:
(6/18) * (5/17) = 30/306 = 5/51
So the probability of selecting two carnations is 5/51.
You sure?
Yes, I am sure.
Okay, thanks!
You're welcome! If you have any other questions, feel free to ask.
I have a question, Mr. Bot.
A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards. Express your answer in percent form rounding to the nearest hundredth.
The probability of drawing a diamond on the first pick is 13/52, or 1/4, since there are 13 diamonds in the deck and 52 total cards. After the first diamond is picked, there are 12 diamonds remaining in the deck out of 51 total cards. Therefore, the probability of drawing another diamond on the second pick, without replacement, is 12/51.
To find the probability of drawing two diamond cards, we multiply the probability of drawing a diamond on the first pick by the probability of drawing a diamond on the second pick:
(13/52) * (12/51) = 156/2652 = 1/17
So the probability of drawing two diamond cards is 1/17 or approximately 0.0588. To express this as a percentage, we multiply by 100:
1/17 * 100 = 5.88% (rounded to the nearest hundredth)
Therefore, the probability of drawing two diamond cards is 5.88%.