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Sagot :
Given:
An archer hits a target 50% of the time.
To find:
The experimental probability that the archer hits the target exactly four of the next five times.
Solution:
It is given that an archer hits a target 50% of the time. It means the probability of hitting the target is
[tex]p=\dfrac{50}{100}[/tex]
[tex]p=0.5[/tex]
The probability of not hitting the target is
[tex]q=1-p[/tex]
[tex]q=1-0.5[/tex]
[tex]q=0.5[/tex]
Binomial distribution formula:
[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]
We need to find the probability that the archer hits the target exactly four of the next five times. So, [tex]n=5,r=4,p=0.5,q=0.5[/tex].
[tex]P(x=4)=^5C_4(0.5)^4(0.5)^{5-4}[/tex]
[tex]P(x=4)=\dfrac{5!}{4!(5-4)!}(0.5)^4(0.5)^{1}[/tex]
[tex]P(x=4)=5(0.5)^{5}[/tex]
[tex]P(x=4)=0.15625[/tex]
Therefore, the experimental probability that the archer hits the target exactly four of the next five times is 0.15625.
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