The probability that a heat-seeking torpedo will hit its target is 0.1 . If the first torpedo hits its target, the probability that the second torpedo will hit the target increases to 0.8 because of the extra heat generated by the first explosion. If two heat-seeking torpedoes are fired at a target, determine the probability that both hit the target. The probability that both torpedos hit the target is (Type an integer or a decimal.)

Step 1 ：The probability that a heat-seeking torpedo will hit its target is 0.1. If the first torpedo hits its target, the probability that the second torpedo will hit the target increases to 0.8 because of the extra heat generated by the first explosion.

Step 2 ：If two heat-seeking torpedoes are fired at a target, we need to determine the probability that both hit the target.

Step 3 ：The probability that both torpedoes hit the target is the product of the probability that the first torpedo hits the target and the probability that the second torpedo hits the target given that the first one has hit. This is because the events are dependent; the outcome of the second event depends on the outcome of the first event.

Step 4 ：Let's denote the probability that the first torpedo hits the target as \(p1 = 0.1\) and the probability that the second torpedo hits the target given that the first one has hit as \(p2_{given_{p1}} = 0.8\).

Step 5 ：The probability that both torpedoes hit the target is then \(p_{both} = p1 \times p2_{given_{p1}} = 0.1 \times 0.8 = 0.08\).

Step 6 ：Final Answer: The probability that both torpedoes hit the target is \(\boxed{0.08}\).