# According to the calculation, the probability of a torpedo hitting a ship is 1/3.

**According to the calculation, the probability of a torpedo hitting a ship is 1/3. How many torpedoes do you need to fire for the probability of at least one hit to be greater than 0.9?**

Let’s solve the inverse problem, namely, calculate how many torpedoes need to be fired so that the probability that no torpedo hits the target is less than 0.1.

In the wording of the condition for this assignment, it is reported that the probability of a torpedo hitting the ship is 1/3.

Therefore, the probability of a torpedo miss is 1 – 1/3 = 2/3.

Then the probability that when 2 torpedoes are launched, both will miss the target, is 2/3 * 2/3 = 4/9> 0/1.

Then the probability that when launching 3 torpedoes everyone will miss the target is 4/9 * 2/3 = 8/27> 0/1.

Then the probability that when launching 4 torpedoes everyone will miss the target is 8/27 * 2/3 = 16/81> 0/1.

Then the probability that, when launching 5 torpedoes, everyone will miss the target is 16/81 * 2/3 = 32/243> 0/1.

Then the probability that when 6 torpedoes are launched, everyone will miss the target is 32/243 * 2/3 = 64/729 <0/1.

Consequently, the probability that when launching 6 torpedoes at least one will hit the target will be greater than 0.9.

Answer: you need to fire 6 torpedoes.