JEE MAIN - Mathematics (2021 - 25th February Morning Shift - No. 1)
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 :
$${3 \over 4}$$
$${3 \over 8}$$
$${1 \over 27}$$
$${1 \over 8}$$
Explanation
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)
= $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$ $$ \times $$ $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$ $$ \times $$ $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$
$$= {1 \over 8}$$
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)
= $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$ $$ \times $$ $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$ $$ \times $$ $${\left( {{2 \over 3} \times {3 \over 4}} \right)} $$
$$= {1 \over 8}$$
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