A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) =
0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise
)
The probability that the student studies for at most two hours is
Show Hint
Always sum all possible probabilities to 1 to find the unknown constant $k$.