If the table below represents a probability model based on observed frequencies, what is the va of x?
Y
C
0.25
A
R
E
S
P(Y)
0.18
0.30
0.17
1
(1 point)
O 0.20
01
Ο 0.01
0.10
To find the expected value of x in this probability model, we need to multiply each value of x by its corresponding probability and then sum up the results.
The values of x are C, A, R, E, and S. The probabilities corresponding to each of these values are 0.25, 0.30, 0.17, 0.18, and 0.10 respectively.
So, the expected value of x is:
E(x) = (0.25 * 0.18) + (0.30 * 0.30) + (0.17 * 0.17) + (0.18 * 1) + (0.10 * 1)
E(x) = 0.045 + 0.09 + 0.0289 + 0.18 + 0.10
E(x) = 0.4439
Therefore, the expected value of x in this probability model is 0.44.
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. (1 point)
Π
To calculate the probability of selecting two carnations, you need to find the total number of ways to choose 2 flowers out of the total number of flowers (18) and the number of ways to choose 2 carnations out of the 6 carnations.
Total number of ways to choose 2 flowers out of 18:
C(18, 2) = 18! / (2! * (18-2)!) = 153
Number of ways to choose 2 carnations out of 6:
C(6, 2) = 6! / (2!*(6-2)!) = 15
So, the probability of selecting two carnations is:
P(selecting two carnations) = Number of ways to choose 2 carnations / Total number of ways to choose 2 flowers
P(selecting two carnations) = 15 / 153
P(selecting two carnations) = 5 / 51
Therefore, the probability of selecting two carnations is 5/51.
Nicole pulls a colored marble out of a bowl, choosing the marble at random. There are 120 marbles in the bowl, of which 80 are black, 28 are white, and the rest are red. Use words and numbers to describe the probability that she will pull a red marble out of the bowl. Show your work. (4 points)
To find the probability that Nicole will pull a red marble out of the bowl, we first need to determine the number of red marbles in the bowl.
Total number of marbles = 120
Number of black marbles = 80
Number of white marbles = 28
Number of red marbles = Total - Black - White = 120 - 80 - 28 = 12
Now that we know there are 12 red marbles, we can calculate the probability of pulling a red marble:
Probability of pulling a red marble = Number of red marbles / Total number of marbles
Probability of pulling a red marble = 12 / 120
Probability of pulling a red marble = 1 / 10
Therefore, the probability that Nicole will pull a red marble out of the bowl is 1/10.