If a discrete random variable X follows uniform distribution and assume only the values 8, 9, 11, 15, 18, 20, the value of P(|X - 14| < 5) will be:
For the discrete uniform distribution on the 6 values \(\{8,9,11,15,18,20\}\), each value has probability \(\tfrac{1}{6}\).
Step 1 — Solve the inequality:
\[|X-14| \lt 5 \iff -5 \lt X-14 \lt 5 \iff 9 \lt X \lt 19\]
Step 2 — Count favourable values: from the support, \(11, 15, 18\) lie in \((9,19)\) — that is 3 values.
Step 3 — Probability:
\[P(|X-14| \lt 5)=\frac{3}{6}=\frac{1}{2}\]
Therefore the answer is \(\dfrac{1}{2}\).
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