JEE Exam > JEE Questions > The probability that a missile hits a target ...
Start Learning for Free
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____
Correct answer is '6'. Can you explain this answer?
Most Upvoted Answer
The probability that a missile hits a target successfully is 0.75. In ...
Let P(r) = probability of r successes
1 – (P(0) + P(1) + P(2)) ≥ 0.95
for n = 5 212 ≤ 102.4 (Not true)
for n = 6 308 ≤ 409.6 true
∴ least value of n = 6
1 – (P(0) + P(1) + P(2)) ≥ 0.95
for n = 5 212 ≤ 102.4 (Not true)
for n = 6 308 ≤ 409.6 true
∴ least value of n = 6
Free Test
FREE
| Start Free Test |
Community Answer
The probability that a missile hits a target successfully is 0.75. In ...
The problem can be solved using the concept of binomial distribution.
Binomial Distribution:
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.
In this case, each missile fired is an independent Bernoulli trial with a probability of success of 0.75. We need at least three successful hits to completely destroy the target.
Probability of at least three successful hits:
To find the probability of at least three successful hits, we need to calculate the probability of exactly three, four, five, and six successful hits and add them together.
- Probability of exactly three successful hits:
P(X = 3) = C(6, 3) * (0.75)^3 * (0.25)^3
= 20 * 0.421875 * 0.015625
= 0.1318359375
- Probability of exactly four successful hits:
P(X = 4) = C(6, 4) * (0.75)^4 * (0.25)^2
= 15 * 0.31640625 * 0.0625
= 0.29541015625
- Probability of exactly five successful hits:
P(X = 5) = C(6, 5) * (0.75)^5 * (0.25)^1
= 6 * 0.2373046875 * 0.25
= 0.35595703125
- Probability of exactly six successful hits:
P(X = 6) = C(6, 6) * (0.75)^6 * (0.25)^0
= 1 * 0.177978515625 * 1
= 0.177978515625
Probability of completely destroying the target:
The probability of completely destroying the target is the sum of the probabilities of at least three successful hits.
P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
= 0.1318359375 + 0.29541015625 + 0.35595703125 + 0.177978515625
= 0.961181640625
Therefore, the probability of completely destroying the target is 0.961181640625, which is greater than 0.95.
Minimum number of missiles:
To find the minimum number of missiles required, we need to find the smallest value of N for which P(X >= 3) is not less than 0.95.
Let's calculate P(X >= 3) for N = 5:
P(X >= 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)
= 1 - C(5, 0) * (0.75)^0 * (0.25)^5 - C(5, 1) * (0.75)^1 * (0.25)^4 - C(5, 2) * (0.75)^2 * (0.25)^3
= 1 -
Binomial Distribution:
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.
In this case, each missile fired is an independent Bernoulli trial with a probability of success of 0.75. We need at least three successful hits to completely destroy the target.
Probability of at least three successful hits:
To find the probability of at least three successful hits, we need to calculate the probability of exactly three, four, five, and six successful hits and add them together.
- Probability of exactly three successful hits:
P(X = 3) = C(6, 3) * (0.75)^3 * (0.25)^3
= 20 * 0.421875 * 0.015625
= 0.1318359375
- Probability of exactly four successful hits:
P(X = 4) = C(6, 4) * (0.75)^4 * (0.25)^2
= 15 * 0.31640625 * 0.0625
= 0.29541015625
- Probability of exactly five successful hits:
P(X = 5) = C(6, 5) * (0.75)^5 * (0.25)^1
= 6 * 0.2373046875 * 0.25
= 0.35595703125
- Probability of exactly six successful hits:
P(X = 6) = C(6, 6) * (0.75)^6 * (0.25)^0
= 1 * 0.177978515625 * 1
= 0.177978515625
Probability of completely destroying the target:
The probability of completely destroying the target is the sum of the probabilities of at least three successful hits.
P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
= 0.1318359375 + 0.29541015625 + 0.35595703125 + 0.177978515625
= 0.961181640625
Therefore, the probability of completely destroying the target is 0.961181640625, which is greater than 0.95.
Minimum number of missiles:
To find the minimum number of missiles required, we need to find the smallest value of N for which P(X >= 3) is not less than 0.95.
Let's calculate P(X >= 3) for N = 5:
P(X >= 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)
= 1 - C(5, 0) * (0.75)^0 * (0.25)^5 - C(5, 1) * (0.75)^1 * (0.25)^4 - C(5, 2) * (0.75)^2 * (0.25)^3
= 1 -
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer?
Question Description
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer?.
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer?.
Solutions for The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer?, a detailed solution for The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? has been provided alongside types of The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____Correct answer is '6'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup