First slide

Theorems of probability

Question

$When a missile is fired from a ship, the probability that it is intercepted is$ $\frac{1}{3}$ $and the probability that the missile hits the target, given that is it not intercepted, is$ $\frac{3}{4}$ $If three missiles are fired independently from the ship, then the probability that all three hit the target, is:$

Moderate

A

$\frac{3}{4}$
B

$\frac{1}{27}$
C

$\frac{3}{28}$
D

$\frac{1}{8}$

Solution

$Probability of hitting the target by one missile is P( hitting when not intercepted)×P(Missile not intercepted) = \frac{1}{2}$
$SInce all the missiles fired independently The probability to hit the target is {(\frac{1}{2})}^{3} = \frac{1}{8}$ $P (missile intercepted) = \frac{1}{3}, P (m i s s i l e n o t i n t e r c e p t e d) = \frac{2}{3} P (h i t t h e t a r g e t) = \frac{3}{4} R e q p r o b a b i l i t y = {(\frac{2}{3} . \frac{3}{4})}^{3} = \frac{1}{8}$

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