Probability of an event =
(number of ways the event can happen) / (total number of possible outcomes) .
Well, the total number of possible outcomes is easy. It's
(6 possibilities for the first cube) x (6 possibilities for the 2nd cube)
= 36 total possible ways for two cubes to roll.
Now, how many of those possibilities show either 4 or 7 ?
Well, here's how a 4 can come up:
1 . . . 3
2 . . . 2
3 . . . 1
and here's how a 7 can come up:
1 . . . 6
2 . . . 5
3 . . . 4
4 . . . 3
5 . . . 2
6 . . . 1 .
So there are 9 ways all together for Lenny to be successful.
The probability is (9/36) .
That's 1/4 , or 25% .
Answer:
Mean = 1.42
Variance = 0.58
Step-by-step explanation:
Given: X denote the number of luxury cars sold in a given day, and Y denote the number of extended warranties sold.
Also, joint probability function of X and Y are given.
To find:
mean and variance of X
Solution:
From the given joint probability function of X and Y,
Mean of X:
Variance of X:
![var(X)=E\left [ X^2 \right ]-\left ( E\left [ X \right ] \right )^2\\=\frac{31}{12}-\left ( \frac{17}{12} \right )^2\\=\frac{31}{12}-\frac{289}{144}\\=\frac{372-289}{144}\\=\frac{83}{144}\\=0.58](https://tex.z-dn.net/?f=var%28X%29%3DE%5Cleft%20%5B%20X%5E2%20%5Cright%20%5D-%5Cleft%20%28%20E%5Cleft%20%5B%20X%20%5Cright%20%5D%20%5Cright%20%29%5E2%5C%5C%3D%5Cfrac%7B31%7D%7B12%7D-%5Cleft%20%28%20%5Cfrac%7B17%7D%7B12%7D%20%5Cright%20%29%5E2%5C%5C%3D%5Cfrac%7B31%7D%7B12%7D-%5Cfrac%7B289%7D%7B144%7D%5C%5C%3D%5Cfrac%7B372-289%7D%7B144%7D%5C%5C%3D%5Cfrac%7B83%7D%7B144%7D%5C%5C%3D0.58)
Answer:
y < 4
Step-by-step explanation:
Since the line is dotted, it will be either greater than or less than depending on if it is shaded above or below. It's "y" because the line crosses the y axis, not the x axis.
Alright, so 3f-g=4 and f+2g=5.
3f-g=4
f+2g=5
Multiplying the first equation by 2 and adding it to the second, we get 7f=13 and by dividing both sides by 7 we get f=13/7. Since f+2g=5, then we can plug 13/7 in for f to get 13/7+2g=5. Next, we subtract 13/7 from both sides to get 2g=3+1/7=22/7 (since 3*7=21 and 21+1=22). DIviding both sides by 2, we get 22/14=g. Plugging that into f/39g, we get (13/7)/(22*39/14)
= (13/7)/(858/14)
= (13/7)*(14/858)
=182/6006
= 91/3003 (by dividing both numbers by 2)
= 13/429 (by dividing both numbers by 7)
= 1/33 (by dividing both numbers by 13)
