Question
Question: The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, ...
The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, then the probability of his shooting the target is
A.1
B.1−(0.7)10
C.(0.7)10
D.(0.3)10
Solution
If p and q be the probability of success and failure of an event respectively. Then the probability of that event getting ‘x’ success in an n-Bernoulli’s trial where (i⩽n), then P(Ax)=nCxpxqn−x.
Complete step-by-step answer:
We do this problem using binomial law, which is, if Ax denotes the event of getting exactly x success in an n-Bernoulli’s trial where (i⩽n), then P(Ax)=nCxpxqn−x, where p and q denotes the probability of success and failure of that event respectively and p+q=1.
Here, p = the probability that a person will hit the target in shooting practice = 0.3
And, q = the probability that a person will not hit a target in shooting practice=1−p=1−0.3=0.7
Here, the total number of shoots is 10 i.e. n=10.
∴The probability that out of 10 shoots none will hit a target=10C0p0q10−0=q10=(0.7)10.
Therefore, the probability of shooting target is 1−(0.7)10
Hence, option (B) is correct.
Note: Another Method –
Let, A be the event that a person will hit a target in shooting practice.
Then the probability of A is given, which is P(A)=0.3.
Now, the probability that a person will not hit a target in shooting practice is P(Aˉ)=1−P(A)=1−0.3=0.7
[ We know P\left( A \right) + P\left( {\bar A} \right) = P\left( X \right) = 1$$$$i.e.,P\left( {\bar A} \right) = 1 - P\left( A \right) ]
Now, the probability that out of 10 shoots none will hit a target is P(Aˉ),P(Aˉ),.....upto10 times = (0.7)10
Therefore, the probability of shooting the target =1−(0.7)10