Consider 16 gallons of genetically modified potatoes. Suppose that 75% of these potatoes have an increased resistance to pests, 50% were engineered to have a longer shelf life, and 30% have an increased resistance to pests and were engineered to have a longer shelf life. If one of these potatoes is randomly selected, compute the probability that this potatoe has an increased resistance to pests, but was not engineered to have a longer shelf life.
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Potatoes have been genetically modified to increase resistance to pests and have a longer shelf life.
Of the potatoes with genetic modifications there is a 75% probability that the resistance to pests has been increased and a 50% probability that the shelf life has been increased. The probability that a potato has an increased resistance to pests and was engineered to have a longer shelf life is 30%.
Of all the potatoes there is a 0.75*0.3 = 22.5% probability that it has both the qualities.
The probability that a potato picked at random has an increased resistance to pests, but was not engineered to have a longer shelf life is 0.75*(0.7) = 0.525
The required probability is 52.5%
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Suppose that 75% of these potatoes have an increased resistance to pests, 50% were engineered to have a longer shelf life, and 30% have an increased resistance to pests and were engineered to have a longer shelf life. If one of these potatoes is randomly selected, compute the probability that this potatoe has an increased resistance to pests, but was not engineered to have a longer shelf life.
A=potatoes have an increased resistance to pests
P(A)=75%=.75
B=potatoes have a longer self life
P(B) =50 %=.50
AB= Potatoes have an increased resistance to pests and were engineered to have a longer shelf life
P(AB) =30% =.30
`A barB=` Potatoes have an increased resistance to pests and were not engineered to have a longer shelf life
`P(A barB)= ?`
where we have difined following terms
`AnnB=AB`
`Ann barB=A barB`
Thus by total probability theorem
`P(A)=P(AB)+P(A barB)`
`.75-.30=P(A barB)`
`P(A barB)=.45`
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