MHT CET · Maths · Probability
The probability distribution of a discrete random variable \(\mathrm{X}\) is
Find the value of \(\mathrm{P}(2 < \mathrm{X} < 6)\)
- A \(\frac{4}{21}\)
- B \(\frac{1}{21}\)
- C \(\frac{10}{21}\)
- D \(\frac{4}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{4}{7}\)
Step-by-step Solution
Detailed explanation
We have \(\mathrm{K}+2 \mathrm{~K}+3 \mathrm{~K}+4 \mathrm{~K}+5 \mathrm{~K}+6 \mathrm{~K}=1 \Rightarrow \mathrm{K}=\frac{1}{21}\)
\(
\begin{aligned}
& \therefore \mathrm{P}(2 < \mathrm{x} < 6)=\mathrm{P}(\mathrm{x}=3)+\mathrm{P}(\mathrm{x}=4)+\mathrm{P}(\mathrm{x}=5) \\
& =\frac{3}{21}+\frac{4}{21}+\frac{5}{21}=\frac{12}{21}=\frac{4}{7}
\end{aligned}
\)
\(
\begin{aligned}
& \therefore \mathrm{P}(2 < \mathrm{x} < 6)=\mathrm{P}(\mathrm{x}=3)+\mathrm{P}(\mathrm{x}=4)+\mathrm{P}(\mathrm{x}=5) \\
& =\frac{3}{21}+\frac{4}{21}+\frac{5}{21}=\frac{12}{21}=\frac{4}{7}
\end{aligned}
\)
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