1.) A certain species of bird has three subspecies in the area. Call these subsp
ID: 3546310 • Letter: 1
Question
1.) A certain species of bird has three subspecies in the area. Call these subspecies A , B, and C. Forty percent of subspecies A has a particular gentic trait. 30% of subspecies B has the trait, and 25% of subspecies Chas the trait. Subspecies A is 20% of the population, subspecies B is 30 % and subspecies C is 50%. If a bird having this trait is captured, what is the probability that it belongs to subspecies A?
2.)Numbers is a game(illegal in the US) where you bet $1.00 on any three- digit number from 000 to 999. If your number come up, you get $1,000.00. Find a Numbers gambler expected winnings for one round of play.
Explanation / Answer
1.) A certain species of bird has three subspecies in the area. Call these subspecies A , B, and C.
Forty percent of subspecies A has a particular gentic trait.
30% of subspecies B has the trait, and 25% of subspecies Chas the trait. Subspecies A is 20% of the population, subspecies B is 30 %
and subspecies C is 50%. If a bird having this trait is captured, what is the probability that it belongs to subspecies A?
Probablity of Population of A = P(A) = 0.2
Probablity of Population of B = P(B) = 0.3
Probablity of Population of C = P(C) = 0.5
Probablity of subspecies A has a particular gentic trait = P(A/T) = 0.4
Probablity of subspecies B has a particular gentic trait = P(B/T) = 0.3
Probablity of subspecies C has a particular gentic trait = P(C/T) = 0.25
using Bayes Theorm.If a bird having this trait is captured, what is the probability that it belongs to subspecies A is P(T/A)
P(T/A) = P(A)(P(A/T)/ (P(A)*P(A/T) + P(B)*P(B/T) + P(C)*P(C/T))
P(T/A) = ( 0.2*0.4) / (0.2*0.4 + 0.3*0.3+0.5*0.25) = 0.08 /(0.08+0.09+0.125) = 0.08/0.295 = 0.2711864406779661
required probablity is 27.11 %
2.)Numbers is a game(illegal in the US) where you bet $1.00 on any three- digit number from 000 to 999. If your number come up,
you get $1,000.00. Find a Numbers gambler expected winnings for one round of play.
probablity of winning = 1/1000 = 0.001
probablity of loosing = 999/1000 = 0.999
winning gives 1000 losing gives -1 thus
expected winnings for one round of play = sum of probablities and thier winning /losing amount thus
expected winnings for one round of play = 0.001*1000+0.999*-1 = 0.001
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