Test Index

Probability Part 1

Section: Mathematics

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Question : 21 of 100

Marks: +1, -0

When a missile is fired from a ship, the probability that it is intercepted is

\;\frac{1}{3}

and the probability that the missile hits the target, given that it is not intercepted, is

\;\frac{3}{4}

. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

[25 Feb 2021 Shift 1]

$\;\frac{1}{27}$
$\;\frac{3}{4}$
$\;\frac{1}{8}$
$\;\frac{3}{8}$

Solution:

Probability of missile to get intercepted

=\;\frac{1}{3}

\therefore

Probability of missile to not get intercepted

=1-\;\frac{1}{3}=\;\frac{2}{3}

Probability of missile to hit the target

=\;\frac{3}{4}

\therefore

Probability of three missiles to hit the target

=\left(\;\frac{2}{3} \times \;\frac{3}{4}\right) \times\left(\;\frac{2}{3} \times \;\frac{3}{4}\right) \times\left(\;\frac{2}{3} \times \;\frac{3}{4}\right)=\;\frac{1}{8}

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