Question 1129928: The probability that a heat-seeking torpedo will hit its target is 0.2. 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, determine the probability that both hit the target. Express your answer as a decimal or integer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability that the torpedo will hit its target is .2.
if the first torpedo hits the target, the probability that the second torpedo will hit the target becomes .7. because the target gets hotter, making it easier for the second torpedo to find the target (these are heat seeking torpedos).
you fire two torpedos.
the probability that they both hit the target is .2 * .7 = .14
the formula used in this case would be:
p(a given b) = p(a and b) / p(b)
p(a given b) is equal to .7
p(b) is equal .2
formula becomes .7 = p(a and b) / .2
solve for p(a and b) to get p(a and b) = .2 * .7 = .14.
that's your answer.
the total probability should be, and is, equal to 1 as shown below:
note that, when the probability of a hit is .2, the probability of a miss is .8.
note also that, when the probability of a hit is .7, the probability of a miss is .3.
here are the total probabilities.
probability of first hit and second miss is .2 * .3 = .06
probability of first hit and second hit is .2 *.7 = .14
probability of first miss and second miss is .8 * .8 = .64
probability of first miss and second hit is .8 * .2 = .16
total probability is equal to .06 + .14 + .64 + .16 = 1.0
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