Explanation Definition: If X is a random variable for the number of successes in n independent and identical repetitions of an experiment with success and failure as two possible outcomes and if p is a probability of success, then the probability for k success is defined as, P ( X = k ) = ( n k ) p k ( 1 − p ) n − k Here, k = 0 , 1 , ⋅ ⋅ ⋅ , n . Calculation: Consider a research which showed that the probability of a missile to penetrate enemy defences and reaches its target is 0.1 . So, p = 0.1 . The smallest number of missiles that are required in order to be 80 % certain of hitting the target at least once is required. This means that P ( X ≥ 1 ) = 0.80 . So, the value of n is required. Define X as random variable which indicates number of identical missiles. Rewrite the probability P ( X ≥ 1 ) = 1 − P ( X < 1 ) and so, P ( X ≥ 1 ) = 1 − P ( X < 1 ) 0.80 = 1 − P ( X < 1 ) P ( X < 1 ) = 1 − 0.80 P ( X < 1 ) = 0.20 Use the probability formula and substitute these values to calculate the smallest number of identical missiles. P ( X = 0 ) = 0

13th Edition

ISBN: 9780357325865

Author: SMITH

Publisher: CENGAGE L

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Chapter 13.6, Problem 53PS

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The smallest number of identical missiles that are required for 80% certainty of hitting the target at least once and if the probability for a missile to penetrate the enemy defence and reach the target is 0.1.

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Chapter 13.6, Problem 52PS

Chapter 13.6, Problem 54PS

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The smallest number of identical missiles that are required for 80 % certainty of hitting the target at least once and if the probability for a missile to penetrate the enemy defence and reach the target is 0.1 .

Solution Summary: The author explains that the probability of a missile to penetrate the enemy defence and reach the target at least once is 0.1.

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To find:

The smallest number of identical missiles that are required for 80% certainty of hitting the target at least once and if the probability for a missile to penetrate the enemy defence and reach the target is 0.1.

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Chapter 13 Solutions

The smallest number of identical missiles that are required for 80 % certainty of hitting the target at least once and if the probability for a missile to penetrate the enemy defence and reach the target is 0.1 .

Solution Summary: The author explains that the probability of a missile to penetrate the enemy defence and reach the target at least once is 0.1.

Concept explainers

Videos

To find: The smallest number of identical missiles that are required for 80% certainty of hitting the target at least once and if the probability for a missile to penetrate the enemy defence and reach the target is 0.1.

Want to see the full answer?

Chapter 13 Solutions

To find:

The smallest number of identical missiles that are required for 80% certainty of hitting the target at least once and if the probability for a missile to penetrate the enemy defence and reach the target is 0.1.