Question

Let $X$ denote the number of hours you study during a randomly selected school day. The probability that $X$ can take the values of $x$, has the following form, where $k$ is some constant
$P(X=x)=\begin{array}{c}\{\begin{array}{cc}0,1& \text{if}x=0\\ Kx& \text{if}x=1\text{or}2\\ K(5-x)& \text{if}x=3\text{or}4\\ 0& \text{otherwise}\end{array}\end{array}$
What is the probability that you study.
For at least two hour.

Answer 1

${\sum }_0^{4}P\left(X\right)=1$

$0.1+k+2k+2k+k=1$

$6k=1-0.1$

$\therefore k=0.15$

$P(X\ge 2)=P(X=2)+P(X=3)+P(X=4)$

$=2k+2k+k$

$=5k$

$=5\left(0.15\right)=0.75$