If random variable X ∼ B n = 5 , p = 1 3 then P 2 X 4 =, 80 243, 40 243, 40 343, 80 343

Given n = 5 p = 1 3 ∴ q = 2 3 P 2 x 4 = P x = 3 = 5 C 3 1 3 3 2 3 2 = 5 × 4 2 × 1 27 × 4 9 = 40 243

If random variable X ∼ B n = 5 , p = 1 3 then P 2 X 4 =

Question: Answered & Verified by Expert

If random variable

X \sim B (n = 5, p = \frac{1}{3})

then

P (2 < X < 4) =

MathematicsProbabilityMHT CETMHT CET 2016

Options:

Solution:

2858 Upvotes Verified Answer

The correct answer is:

\frac{40}{243}

Given

n = 5

p = \frac{1}{3}

∴ q = \frac{2}{3}

P (2 < x < 4) = P (x = 3)

=^{5} C_{3} {(\frac{1}{3})}^{3} {(\frac{2}{3})}^{2}

= \frac{5 \times 4}{2} \times \frac{1}{27} \times \frac{4}{9}

= \frac{40}{243}

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