Question
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The probability that an archer hits the target is p= 0.8, so the probability that he misses the target is q = 0.2. It is known that in this situation the probability that the archer hits the target exactly r times in n attempts is given by the term containing pr in the binomial expansion of (p + q)n.
Find the probability that the archer hits the target exactly four times in six attempts
The probability that an archer hits the target is p= 0.8, so the probability that he misses the target is q = 0.2. It is known that in this situation the probability that the archer hits the target exactly r times in n attempts is given by the term containing pr in the binomial expansion of (p + q)n.
Find the probability that the archer hits the target exactly four times in six attempts
Answers
Steve
well, they tell you that
the probability that the archer hits the target exactly r times in n attempts is given by the term containing p^r in the binomial expansion of (p+q)^n
You have p=0.8 and q=0.2
You want the term containing p^4 in the expansion of (p+q)^6
That term will be C(6,2)p^4q^2
= 15(.8^4)(.2^2) = 0.25
the probability that the archer hits the target exactly r times in n attempts is given by the term containing p^r in the binomial expansion of (p+q)^n
You have p=0.8 and q=0.2
You want the term containing p^4 in the expansion of (p+q)^6
That term will be C(6,2)p^4q^2
= 15(.8^4)(.2^2) = 0.25