An experiment is performed as follows, A fair 6 sided die is rolled to determine

Question

An experiment is performed as follows, A fair 6 sided die is rolled to determine which of two coins to flip. If a 6 is rolled, then an unbalanced coin that has P(heads) = 0.9 is flipped. If a 6 is not rolled, then a fair coin is flipped.

a) If the flipped coin lands heads, what is the probability that when the die was rolled it landed on a 6?(A tree diagram may be helpful)

b) If this experiment is performed 50 times, and X denotes the number of times the result is heads, calculate E(3X+1).

c) Why can a poisson distribution not be used to estimate the X defined in part (b)?

Explanation / Answer

a) here let probabilty that on adie 6 comes =P(DS) =1/6

and not coming 6 =P(DNS) =5/6

let probabilty of head =P(H)

a) hence P(H) =P(DS)*P(H|DS) +P(DNS)*P(H|DNS) =(1/6)*0.9+(5/6)*0.5 =0.5667

probability that when the die was rolled it landed on a 6, given it flipped heads =P(DS|H) =P(DS)*P(H|DS)/P(H)

=(1/6)*(0.9)/0.5667=0.2647

b)as probabilty of coming head =0.5667

hence in 50 times expected X =np =50*0.5667 =28.33

therefore E(3X+1) =3*E(X)+1 =3*28.33+1 =86

c) as probabilty is fixed here for a trail , hence we can not use poisson approximation.also for poisson p value should be very less and n should be very large.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.