Determine the probability that the student studied for at most 2 hours.
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Solution and Explanation
Step 1: The probability that the student studied for at most 2 hours is given by: \[ P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2). \] Step 2: Substitute the given values: \[ P(X \leq 2) = 0.1 + k(1) + k(2). \] Step 3: Substitute \( k = 0.15 \): \[ P(X \leq 2) = 0.1 + 0.15(1) + 0.15(2). \] Step 4: Compute the value: \[ P(X \leq 2) = 0.1 + 0.15 + 0.3 = 0.55. \] Thus, the probability that the student studied for at most 2 hours is 0.55.
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