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6. A submarine attempts to sink an aircraft carrier. It will be successful only if two or more torpedoes hit the carrier. If the probability of a hit is 40% for each torpedo, what is the probability that the carrier will be sunk if the: a. Submarine fires two torpedoes? b. Submarine fires three torpedoes? c. Submarine fires four torpedoes? 7. A precision guided munition has a Circular Error Probability at 66.67% of 10m. This means that 2/3rds of all hits are within 10m of the target. A series of six test drops have been made. a. Find the probability that none of the weapons hit within 10m of the target. b. Find the probability that at least one weapon hit within 10m of the target. c. The weapons test is successful if the probability is 90% that three or more weapons will hit within 10m of the target. Is the test successful?

          6. A submarine attempts to sink an aircraft carrier. It will be successful only if two or more
torpedoes hit the carrier. If the probability of a hit is 40% for each torpedo, what is the
probability that the carrier will be sunk if the:
a. Submarine fires two torpedoes?
b. Submarine fires three torpedoes?
c. Submarine fires four torpedoes?
7. A precision guided munition has a Circular Error Probability at 66.67% of 10m. This means that
2/3rds of all hits are within 10m of the target. A series of six test drops have been made.
a. Find the probability that none of the weapons hit within 10m of the target.
b. Find the probability that at least one weapon hit within 10m of the target.
c. The weapons test is successful if the probability is 90% that three or more weapons will
hit within 10m of the target. Is the test successful?

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6. A submarine attempts to sink an aircraft carrier. It will be successful only if two or more
torpedoes hit the carrier. If the probability of a hit is 40% for each torpedo, what is the
probability that the carrier will be sunk if the:
a. Submarine fires two torpedoes?
b. Submarine fires three torpedoes?
c. Submarine fires four torpedoes?
7. A precision guided munition has a Circular Error Probability at 66.67% of 10m. This means that
2/3rds of all hits are within 10m of the target. A series of six test drops have been made.
a. Find the probability that none of the weapons hit within 10m of the target.
b. Find the probability that at least one weapon hit within 10m of the target.
c. The weapons test is successful if the probability is 90% that three or more weapons will
hit within 10m of the target. Is the test successful?

Added by Jason M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

09/06/2023

Step 1

Submarine fires two torpedoes: We need at least two torpedoes to hit the carrier. Since there are only two torpedoes, both must hit the carrier. The probability of each torpedo hitting is 0.4. So, the probability of both hitting is: $P(2 \text{ hits}) = 0.4 Show more…

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Submarine attempts to sink an aircraft carrier will be successful only if two or more torpedoes hit the carrier. The probability of a hit is 40% for each torpedo. What is the probability that the carrier will be sunk if the submarine fires two torpedoes? What is the probability if the submarine fires three torpedoes? What is the probability if the submarine fires four torpedoes? Precision guided munition has a Circular Error Probability of 66.67% at 10m. This means that 2/3 of all hits are within 10m of the target. A series of six test drops have been made. Find the probability that none of the weapons hit within 10m of the target. Find the probability that at least one weapon hit within 10m of the target. Is the test successful if the probability is 90% that three or more weapons will hit within 10m of the target?

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Transcript

00:01 So we have the success on this first question of having two or more torpedoes hit.

00:06 And that would mean it would be sunk.

00:08 So we want, if two are fired, the likelihood of being sunk is to have a hit and a hit, so .16.

00:17 Now, if we're going to have fire three, we could have two hit, or we could have all three hit.

00:24 And if we have two hit, that means one also misses.

00:26 So that is binomial probability.

00:29 And we have that 3 choose 2 times the probability of success to the second times the probability of a failure.

00:36 Or, we can have all three hit.

00:39 And when we do that calculation, it comes out to be about a 35 % chance.

00:44 And then finally, we're now just increasing the number of torpedoes that are being fired.

00:53 Now we're up to n being 4.

00:56 So this, again, is a binomial setting.

00:58 And we want to have two or more hit.

01:02 So that's going to be 2, 3, or 4.

01:04 And we could find those three probabilities and add them together.

01:07 Or, i'm going to use my binomial cdf.

01:10 The complement of two or more is one or less.

01:14 So that is 0 and 1.

01:16 And this binomial cdf will do that calculation for me.

01:20 And that comes out to be about 52 .5%...

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