Question

The probability that a marksman will hit a target is given as $\dfrac{1}{5}$. Then his probability of at least one hit in 10 shoots is
A) $1 - {\left( {\dfrac{4}{5}} \right)^{10}}$
B) $\dfrac{1}{{{5^{10}}}}$
C) $1 - \left( {\dfrac{1}{{{5^{10}}}}} \right)$
D) None of these

Answer 1

Hint:Given, the probability that a marksman will hit a target is given as $\dfrac{1}{5}$.Firstly we will find the probability that the marksman will not hit a target. Then, we will find the probability that he will not hit a target in ten shoots. Lastly, we will find the required probability.

Formula Used: $P(E') = 1 - P(E)$

Complete step by step Solution:
Given, the probability that a marksman will hit a target is given as $\dfrac{1}{5}$
Let E be the event that marksman will hit a target.
$ \Rightarrow P(E) = \dfrac{1}{5}$
The probability that marksman will not hit a target $P(E') = 1 - P(E)$
$P(E') = 1 - \dfrac{1}{5}$
$ \Rightarrow P(E') = \dfrac{4}{5}$
Probability that he will not hit a target in ten shoots$ = {(P(E'))^{10}}$
$ = {\left( {\dfrac{4}{5}} \right)^{10}}$
Probability that at least one hit in 10 shoots$ = 1 - {\left( {\dfrac{4}{5}} \right)^{10}}$

Hence, the correct option is (A).

Additional Information:
Probability suggests that chance. It's a branch of arithmetic that deals with the incidence of a random event. the worth is expressed from zero to at least one. likelihood has been introduced in Maths to predict however possible events are to happen. That means the likelihood is essentially the extent to which one thing is probably going to happen. This can be the essential applied math that is additionally employed in the likelihood distribution, wherever you'll learn the likelihood of outcomes for a random experiment. to search out the likelihood of one event occurring, first, we must always understand the full range of potential outcomes.

Note:Students can make mistakes while the probability that marksman will not hit a target. So should pay attention while finding the same. Then, they should find the probability that he will not hit a target in ten shots correctly to get the correct answer.