A bowl contains 10 jellybeans (4 red, 1 blue, and 5 white). If you pick 3 jellybeans from the bowl at random and without replacement, what is the probability that exactly 2 will be red? Express in a common fraction.
possible outcomes are (R = red, N = nonred)
RRN ---- (4/10)(3/9)(6/8)= 1/10
RNR ---- same or 1/10
NRR ---- same or 1/10
so prob of 2reds, one different = 3/10
or, using combinations
C(4,2)xC(6,1)/C(10,3)
= 6x6/120 = 3/10
Well, since I am a Clown Bot, I must clown around with numbers too! Let's do some funny math.
To find the probability, we need to figure out the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways you can choose 3 jellybeans from a total of 10, which is given by the binomial coefficient (10 choose 3). Using some clown magic, we can calculate this as:
10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.
Now, let's find the number of favorable outcomes. We want exactly 2 red jellybeans, which can be chosen in (4 choose 2) ways:
4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6.
So, the number of favorable outcomes is 6.
Thus, the probability of picking exactly 2 red jellybeans is 6/120, which simplifies to 1/20.
That means you have a 1 in 20 chance of picking exactly 2 red jellybeans! Good luck, and remember, laughter is the best antidote for jellybeans!
To find the probability that exactly 2 jellybeans will be red, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
First, let's calculate the total number of possible outcomes. Since we pick 3 jellybeans without replacement, the total number of possible outcomes is the total number of ways to choose 3 jellybeans from the bowl, which can be calculated using combinations.
The total number of possible outcomes = C(10, 3) = 10! / (3! * (10 - 3)!) = 120.
Next, we need to calculate the number of favorable outcomes, which is the number of ways to choose 2 red jellybeans and 1 jellybean that is not red (either blue or white).
The number of ways to choose 2 red jellybeans = C(4, 2) = 4! / (2! * (4 - 2)!) = 6.
The number of ways to choose 1 non-red jellybean = C(6, 1) = 6! / (1! * (6 - 1)!) = 6.
Therefore, the number of favorable outcomes = (number of ways to choose 2 red jellybeans) * (number of ways to choose 1 non-red jellybean) = 6 * 6 = 36.
Finally, we can calculate the probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 36 / 120 = 3 / 10.
Therefore, the probability that exactly 2 jellybeans will be red is 3/10.
To find the probability of exactly 2 red jellybeans out of 3, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the total number of possible outcomes. When you pick the first jellybean, there are 10 options. When you pick the second jellybean, there are then 9 remaining options. Finally, for the third jellybean, there are 8 remaining options. Therefore, the total number of possible outcomes is 10 * 9 * 8 = 720.
Next, let's determine the number of favorable outcomes. To have exactly 2 red jellybeans, we have to consider the different combinations of picking 2 red jellybeans from the 4 available. This can be calculated using combinations. The number of ways to choose 2 jellybeans from 4 is denoted as C(4, 2) and calculated as C(4, 2) = 4! / (2! * (4 - 2)!) = (4 * 3) / (2 * 1) = 6.
Additionally, for the third jellybean, we can choose any of the remaining 8 non-red jellybeans. Therefore, the total number of favorable outcomes is 6 * 8 = 48.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 48 / 720 = 1 / 15.
Hence, the probability of picking exactly 2 red jellybeans is 1/15.