csat-suneung 2008 Q8

csat-suneung · South-Korea · csat__math-humanities 3 marks Continuous Probability Distributions and Random Variables PDF Graph Interpretation and Probability Computation

A continuous random variable $X$ has a range of $0 \leqq X \leqq 3$, and the probabilities $\mathrm { P } ( X \leqq 1 )$ and $\mathrm { P } ( X \leqq 2 )$ are the two roots of the quadratic equation $6 x ^ { 2 } - 5 x + 1 = 0$. What is the value of the probability $\mathrm { P } ( 1 < X \leqq 2 )$? [3 points]
(1) $\frac { 1 } { 12 }$
(2) $\frac { 1 } { 6 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 3 }$
(5) $\frac { 5 } { 12 }$

A continuous random variable $X$ has a range of $0 \leqq X \leqq 3$, and the probabilities $\mathrm { P } ( X \leqq 1 )$ and $\mathrm { P } ( X \leqq 2 )$ are the two roots of the quadratic equation $6 x ^ { 2 } - 5 x + 1 = 0$. What is the value of the probability $\mathrm { P } ( 1 < X \leqq 2 )$? [3 points]\\
(1) $\frac { 1 } { 12 }$\\
(2) $\frac { 1 } { 6 }$\\
(3) $\frac { 1 } { 4 }$\\
(4) $\frac { 1 } { 3 }$\\
(5) $\frac { 5 } { 12 }$

Paper Questions

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