Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the values $x_i$ has the following form, where k is some unknown constant.
$P(X = x;) =\left\{\begin{matrix}0.2,&if\,x_i=0\\Kx_i,& if\, x_i = 1\, or\, 2\\k (5-x_i),&if\, x_i = 3\\0,&otherwise\end{matrix}\right.$
What is the probability that the person watches atmost two hours of television on a selected day?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{17}{25}$
From the given information, we find that the probability distribution of X is
|
X |
0 |
1 |
2 |
3 |
|
P(X) |
0.2 |
k |
2k |
2k |
We know that $Σp_i = 1$
$⇒ 0.2+k+2k + 2k = 1$
$⇒ 5k=0.8⇒k=\frac{4}{25}$
P(the person watches atmost two hours of television)
$= P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)$
$= 0.2 + k + 2k$
$= 0.2 + 3k =\frac{1}{5}+\frac{12}{25}=\frac{17}{25}$