Answer:
The probability that he or she is high-risk is 0.50
Step-by-step explanation:
P(Low risk) = 40% = 0.40
P( Moderate risk) = 40% = 0.40
P(High risk) = 20% = 0.20
P(At - fault accident | Low risk) = 0% = 0
P(At-fault accident | Moderate risk) = 10% = 0.10
P(At-fault accident | High risk) = 20% = 0.20
If a driver has an at-fault accident in the next year, what is the probability that he or she is high-risk. Hence, We need to calculate P( High risk | at-fault accident) = ?
Using Bayes' conditional probability theorem
P( High risk | at-fault accident) = ( P( High risk) * P(At-fault accident | High risk) ) / { P( Low risk) * P(At-fault accident | Low risk) +P( Moderate risk) * P(At-fault accident | Moderate risk) + P( High risk) * P(At-fault accident | High risk) }
P( High risk | at-fault accident)= (0.20 * 0.20) / ( 0.40 * 0 + 0.40 * 0.10 + 0.20 * 0.20 )
P( High risk | at-fault accident) = 0.04 / 0 + 0.04 + 0.04
P( High risk | at-fault accident) = 0.04 / 0.08
P( High risk | at-fault accident) = 0.50
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