1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
loris [4]
2 years ago
6

Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targete

d and destroyed, what is the probability that more than 1 vessel transporting nuclear weapons was destroyed
Mathematics
1 answer:
icang [17]2 years ago
8 0

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

Fleet of 17 means that N = 17

4 are carrying nucleas weapons, which means that k = 4

9 are destroyed, which means that n = 9

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

P(X > 1) = 1 - P(X \leq 1)

In which

P(X \leq 1) = P(X = 0) + P(X = 1)

So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294

P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118

Then

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412

P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

You might be interested in
True or false and if false what would be the correct term be?
vagabundo [1.1K]
It’s True.. you take the “extreme” variable from each proportion and cross multiply them before setting them equal to the product of the two “means” (which are just the other 2 numbers in the proportions).
3 0
3 years ago
Prime factorization of 43
Volgvan

Answer:

Step-by-step explanation:

Prime factorization: 43 is prime. The exponent of prime number 43 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 43 has exactly 2 factors.

8 0
2 years ago
A sweater with a regular price of $38.50 is on sale for 30% off. Find the final
Paraphin [41]

Answer:

The final price would be $26.95

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What are the prime numbers​
AysviL [449]
Prime numbers are only divisible by 1 or itself; the first few are are 2, 3, 5, 7, and 11.
5 0
3 years ago
Read 2 more answers
A group of students went on a field trip. There were 3 boys for every 4 girls in the group. If there were 20 girls, how many stu
guajiro [1.7K]

Answer:

35 students

Step-by-step explanation:

So if every 3 boys there is 4 girls you can solve that there is 5 times the amount of girls to get to 20. So to solve for the boys you do the same.

3 x 5 = 15

That means there are 15 boys and 20 girls but we want to know the total so what you do is just add 15+20=35

So 35 total students.

Hope that helps and have a great day!

4 0
3 years ago
Other questions:
  • A class voted for either rollerblading, swimming, or biking as their favorite summer activity. If swimming got 42% percent of th
    11·1 answer
  • I'm trying to find out if the system have a unique solution, no solution or infinitely many solutions
    12·2 answers
  • ben has agreed to play fewer video games and spend more time studying. he has agreed to play less than 10 hours of video games e
    12·1 answer
  • I’ll cash app 20 and 50 points text me after you answer.
    15·2 answers
  • 100 POINTS
    6·2 answers
  • What is 26% of 200.i really need to know
    9·2 answers
  • NEED HELP QUICK!!
    14·1 answer
  • Can someone help me on this too!
    13·2 answers
  • The length of the base of an isosceles triangle is x. The length of a leg is 3x - 6. The perimeter of the triangle is 58. Find x
    12·1 answer
  • Please help asap will give lots of points
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!