Let Z denote the number of hours you study on a Monday. It is known that P(Z=0) = 0.4 , P(Z=1 or 2) = kz (where k is constant), and P(Z) = 0 otherwise - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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Let Z denote the number of hours you study on a Monday. It is known that P (Z = 0) = 0.4, P (Z = 1 or 2) = k z (where k is constant), and P (Z) = 0 otherwise. What is the probability that you study at least two hours?

Solution & Step-by-step Explanation

The sum of all probabilities must be 1. P (0) + P (1) + P (2) = 1 Given P (0) = 0.4, P (1) = k (1) = k, and P (2) = k (2) = 2 k . 0.4 + k + 2 k = 1 3 k = 0.6 ⟹ k = 0.2 The probability of studying at least two hours is P (Z \geq 2) . In this distribution, that is just P (2) : P (2) = 2 k = 2 (0.2) = 0.4

Try it yourself before checking the explanation above.

Let Z denote the number of hours you study on a Monday. It is known that P (Z = 0) = 0.4, P (Z = 1 or 2) = k z (where k is constant), and P (Z) = 0 otherwise. What is the probability that you study at least two hours?

0.5

0.1

0.4

0.3

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