The probability that missile will strike the target is 1/5 . If six such missiles are fired, then the probability that exactly two missiles will strike the target is
Answers
Answer:
175/256
Step-by-step explanation:
Required probability =1 − probability that target won
′
t be hit
∴ probability =1− (
4
3
)
4
=1−
256
81
=
256
175
Concept:
In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value. A Bernoulli trial or experiment is another name for a single success or failure test, while a Bernoulli process is another name for a sequence of results. The binomial distribution is a Bernoulli distribution for n = 1, or one experiment. The renowned binomial test of statistical significance is built on the binomial distribution.
Given:
The probability that missile will strike the target is 1/5 . If six such missiles are fired,
Find:
Probability of exactly two missiles will strike the target
Solution:
P( missile will hit)= 1/5
P( missile will not hit)= 4/5
Using binomial distribution,
P(exactly two missiles will strike the target)=⁶C₂(1/5)²(4/5)⁴
=0.245
Therefore, probability of exactly two missiles will strike the target is 0.245
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