Question

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 0.7 because of the extra heat generated by the first explosion. If two heat-seeking torpedoes are fired at a target, what is the probability that both hit the target?

Answer 1

The probability that two heat-seeking torpedoes will both hit the target, given the first has a 10% chance and the second a 70% chance following a first hit, is 7%.

Step-by-step explanation:

The student asks about the probability of two heat-seeking torpedoes hitting their target given the probabilities for each hit depend on the previous hit. Since the first torpedo has a probability of 0.1 (10%) of hitting its target, and the second torpedoe's probability increases to 0.7 (70%) conditional on the first hit, the combined probability of both torpedoes hitting the target is the product of the two probabilities.

To find the overall probability of both events occurring, we multiply the independent probability of the first hit by the conditional probability of the second hit, assuming the first was a hit:

• Probability of first hit (P(A)) = 0.1
• Probability of second hit given first hit (P(B|A)) = 0.7
• Total probability of both hits (P(A) × P(B|A)) = 0.1 × 0.7 = 0.07

Thus, the probability that both heat-seeking torpedoes hit the target is 0.07, or 7%.