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Questions  >>  CBSE XII  >>  Math  >>  Model Papers
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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. \[ p(X=x) = \left\{ \begin{array}{l l}0.1, & \quad if{ x = 0}\\ kx, & \quad if{ x = 1 \: or\: 2} \\ k(5-x), & \quad if{ x = 3 \: or\: 5} \\ 0, & \quad \: otherwise \end{array}. \right. \] (i) Find the value of K (ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours?

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A)
Since the sum of individual probabilities must be equal to 1 So, P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) = 1 0.1+K+2K+2K+K=1 6K=0.9 K=0.15 Once we get the value of K we can calculate the required probabilitues using binomial trials.
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