suppose that youencounter two traffic lights on your commute to school. Based onpast experience, you judge that the probability is .60 that thefirst light will be red when you get to it, .50 that the secondlight will be red, and .40 that both lights will be red.
a)Determine the conditional probability that the second lightwill be red, given that the first light is red. (Here andthroughout, show the details of your calculations.)
b)Are the events {first light is red} and {second light is red}independent? Justify your answer.
c) Given that at least one light is red, what is the probabilitythat both lights are red? (Show your work.)
