Volunteers were asked to fill out a survey about body piercings and tattoos. The probability that a person has a tattoo is 0.3. For this problem, we can assume that the volunteers are independent.
a) What is the probability that three people will have a tattoo out of 10 volunteers surveyed?
b) How many volunteers out of 10 can we expect to have a tattoo?
c) What is the probability that it will take asking at least 3 volunteers to find the first person to have a tattoo?
d) How many volunteers should we expect to ask to find the first one that has a tattoo?
e) What is the probability that it will take asking at least 5 volunteers to find the third person to have a tattoo?
f) How many volunteers should we expect to ask to find three people who have a tattoo?
a)
probability that three people will have a tattoo out of 10 volunteers surveyed
=10C3(0.3)3*(0.7)7=0.266828
b)
expected number =np=10*0.3=3
c)
probability that it will take asking at least 3 volunteers to find the first person to have a tattoo
=P(first 2 person not have tattoo)=(0.7)2 =0.49
d)
expect to ask to find the first one that has a tattoo =1/p=1/0.3=3.33
e)
probability that it will take asking at least 5 volunteers to find the third person to have a tattoo
=P(at most 2 person have tattoo in first 4)=P(X=0)+P(X=1)+P(X=2)
=4C0*(0.3)0(0.7)4+4C1*(0.3)1(0.7)3+4C2*(0.3)2(0.7)2 =0.9163
f)
expected value =r/p=3/0.3 =10
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