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Let denote the number of hours you study during a randomly selected school day. The probability…
Let $X$ denote the number of hours you study during a randomly selected school day. The probability that $X$ can take the values '$x$' has the following form, where '$k$' is some unknown constant.
$P(X = x) = \begin{cases} 0.1, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } 2 \\ k(5-x), & \text{if } x = 3 \text{ or } 4 \\ 0, & \text{otherwise} \end{cases}$
(a)[1.0]
Find the value of '$k$'.
(b)[3.0]
What is the probability that you study:
(i) at least two hours?
(ii) exactly two hours?
(iii) at most 2 hours?
Answer
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From ISC 2018 Specimen Mathematics Paper 1, question 10.