When a missile is fired from a ship, the probability that it is intercepted is [1 3] and t…

Question

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

Accepted Answer

Probability of not getting intercepted = $${2 \over 3}$$

When it is not intercepted, probability of missile hitting target = $${3 \over 4}$$

$$\therefore$$ So when such 3 missiles launched
then P (all 3 hitting the target)

= $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$ $$ \times $$ $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$ $$ \times $$ $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$

$$= {1 \over 8}$$

Solutions · 1