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# Said a teacher to young Johnny, 'If a certain missle will hit its target one out of four times, and four such missles are fired at one target, then what is the probability that the target will be hit...' 'That's simple,' answered Johnny. 'It's a certainty that one missle will land on target.' What do you the read have to say about that?

Question #24213. Asked by Jake. (Nov 13 02 11:05 AM)

tented

Each missile will have a 25% chance of success - that will not increase of decrease with the number fired as the average is taken over a huge number. Hence it is possible for all 4 to hit or indeed none.

 Nov 13 02, 11:29 AM
greencavalier

Probability of 4 misses is 0.75*0.75*0.75*0.75 = 0.316-ish
So probability of at least one hit is 1-0.316 = 0.684, about 68%.

 Nov 13 02, 12:48 PM
Andy

Johnny's assumption is wrong, and I would be willing to place money against him. You have four chances to hit the target, a statistically low number, and a 75% failure rate to boot. It's like when you buy a coke and it says 1 in 6 chance of winning another Coke. I guarantee if you buy six cokes, I would be surprised if you indeed won a free Coke.

 Nov 13 02, 6:35 PM
frognut

a 3/4 probability of one shot missing
to the power of four for four shots missing= 81 / 256
subtracted from one for probability of a hit = 175 / 256
or probability of 68.359375 % for one or more hits

 Nov 19 02, 12:26 AM

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