Mike encounters two traffic lights on his way to school in the morning. On a good day the first light is red with a probability 0.7 and green with a probability 0.3. On a bad day he gets a red or green light with equal probabilities. The probability of being stopped by a red light at the second traffic light is the same as the probability at the first light. With a probability 0.6, he will have a good day, and with a probability 0.4 he will have a bad day. (a) What is the probability that Mike will drive to school without having to stop at a traffic light