Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a he
1 answer:
A) Sample size of compound event = 25
B) New Sample size = 36.
What is Compound event?
A compound event is one that has more than one sample point. Simple events are less complicated than compound events. These occurrences entail the possibility of multiple occurrences. One is the probability of all possible outcomes of a compound event.
An event that consists of two or more simple events is called a compound event. Simple events are those that can only have one result, whereas complex events can have a variety of distinct results. Compound events can consist of several independent or dependent occurrences, where the result of one event has no bearing on the likelihood of the other.
Given,
Number of buttons in a container = 5
Lucas picks one button, replaces it and then picks another.
Therefore,
Sample size of the compound event
n =
n =
Now, one more button is added in the container and in total there are 6 buttons.
Lucas repeats the same process again and hence,
Sample size of the new compound event will be,
n =
n =
Full Question is - Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is ___ Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be ____
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Given
We can rewrite it in matrix form as:
![\left[\begin{array}{cccc}1&-1&2&4\\5&2&-1&3\\0&0&0&0\\0&0&0&0\end{array}\right] \left[\begin{array}{c}w\\x\\y\\z\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right] \\ \\ \left[\begin{array}{cccc}1&-1&2&4\\5&2&-1&3\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right]\ \ \ \ \ -5R_1+R_2\rightarrow R_2](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C5%262%26-1%263%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dw%5C%5Cx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%20%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C5%262%26-1%263%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%20%5C%20%5C%20%5C%20%5C%20-5R_1%2BR_2%5Crightarrow%20R_2)
![\left[\begin{array}{cccc}1&-1&2&4\\0&7&-11&-17\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right]\ \ \ \ \ \frac{1}{7} R_2\rightarrow R_2 \\ \\ \left[\begin{array}{cccc}1&-1&2&4\\0&1&-\frac{11}{7}&-\frac{17}{7}\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right]\ \ \ \ \ R_1+R_2\rightarrow R_1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C0%267%26-11%26-17%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%20%5C%20%5C%20%5C%20%5C%20%20%5Cfrac%7B1%7D%7B7%7D%20R_2%5Crightarrow%20R_2%20%5C%5C%20%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C0%261%26-%5Cfrac%7B11%7D%7B7%7D%26-%5Cfrac%7B17%7D%7B7%7D%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%20%5C%20%5C%20%5C%20%5C%20R_1%2BR_2%5Crightarrow%20R_1)
![\\ \\ \left[\begin{array}{cccc}1&0&\frac{3}{7}&\frac{11}{7}\\0&1&-\frac{11}{7}&-\frac{17}{7}\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right] \\ \\ \Rightarrow w= -\frac{3}{7} y- \frac{11}{7} z \\ x=\frac{11}{7} y+ \frac{17}{7} z \\ y=free \\ z=free \\ \\ =y\left\ \textless \ -\frac{3}{7},\frac{11}{7}1,0\right\ \textgreater \ +z\left\ \textless \ - \frac{11}{7},\frac{17}{7},0,1\right\ \textgreater \](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26%5Cfrac%7B3%7D%7B7%7D%26%5Cfrac%7B11%7D%7B7%7D%5C%5C0%261%26-%5Cfrac%7B11%7D%7B7%7D%26-%5Cfrac%7B17%7D%7B7%7D%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20w%3D%20-%5Cfrac%7B3%7D%7B7%7D%20y-%20%5Cfrac%7B11%7D%7B7%7D%20z%20%5C%5C%20x%3D%5Cfrac%7B11%7D%7B7%7D%20y%2B%20%5Cfrac%7B17%7D%7B7%7D%20z%20%5C%5C%20y%3Dfree%20%5C%5C%20z%3Dfree%20%5C%5C%20%20%5C%5C%20%3Dy%5Cleft%5C%20%5Ctextless%20%5C%20-%5Cfrac%7B3%7D%7B7%7D%2C%5Cfrac%7B11%7D%7B7%7D1%2C0%5Cright%5C%20%5Ctextgreater%20%5C%20%2Bz%5Cleft%5C%20%5Ctextless%20%5C%20-%20%5Cfrac%7B11%7D%7B7%7D%2C%5Cfrac%7B17%7D%7B7%7D%2C0%2C1%5Cright%5C%20%5Ctextgreater%20%5C%20)
Thus, the solution set is a span of
We can rewrite it in matrix form as:
Thus, the solution set is a span of