A student was doing a project work, involving a school survey, to find the number of hours spent on study by students on a randomly selected school day. At the end of the survey he prepared the following report related to the data.
Let x denote the number of hours spent on study by students on a randomly selected school day
then,
\(P(X = x) = \begin{cases} 0.2, & \text{if } x = 0\\ kx, & \text{if } x = 1 \text{ or } x = 2\\ k(6 - x), & \text{if } x = 3 \text{ or } x = 4\\ 0, & \text{otherwise} \end{cases}\)
where k is unknown constant
Based on the above information answer the Questions
The probability that the study time of students is at least 1 hour
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.8
“At least 1 hour” is every case except X = 0, so use the complement:
\(P(X \ge 1) = 1 - P(X = 0)\)
\(= 1 - 0.2 = 0.8\)