Question

Speed detector determines whether the driver has exceeded the speed limit. It is known that PAI B) = P(ALB9 = p. Let's define event A as "detector shows that limit has been broken, and "speedometer in the driver's car indicates that the speed has been exceeded". It is known that P(B) 0.05. 4. a. In your own words, what is P(BIA)? b. Calculate P(BCIA) if p 0.95. c. How big should p be so that P(B|A) 0.9? OW

Answer 1

a)P(B^c|A) represent the probability that speedometer does not indicate the speed has been exceeded given detector shows the speed has been exceeded,

b)

P(B^c|A)=P(Bc)*P(A|Bc)/(P(Bc)*P(A|Bc)+P(B)*P(A|B))=(1-0.05)*(1-0.95)/((1-0.05)*(1-0.95)+0.05*0.95))

=0.5

c)

here P(B|A)=P(B)*P(A|B)/(P(Bc)*P(A|Bc)+P(B)*P(A|B))

0.9=0.05*p/(0.95*(1-p)+0.05p)

0.9*(0.95-0.9p)=0.05p

p=0.9942