Question

A gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy will hit the target?

• A. 0.036
• B. 0.225
• C. 0.964
• D. 0.775
• E. None of these

Answer 1

The correct option is C

0.964

The enemy aircraft will be brought down even if one of the four shots hit the aircraft.

The opposite of this situation is that none of the four shots hit the aircraft.

The probability that none of the four shots hit the aircraft is given by:

(1-0.7)(1-0.6)(1-0.5)(1-0.4) = 0.3$\times$0.4$\times$0.5$\times$0.6 = 0.036

So, the probability that at least one of the four shots hit the aircraft:

=1-0.036 = 0.964