A bin contains 3 types of flashlights (Type 1, Type 2, and Type 3.) The probability that a Type 1flashlight will give more than 100 hours of use is 0.7. The corresponding probabilities for Types 2 and 3are 0.4 and 0.3 respectively. Furthermore, assume that 20% of the bin contains Type 1 flashlights, 30% Type 2, and 50% Type 3 flashlights. (a) What is the probability that a randomly chosen flashlight will give more than 100 hours of use? (b) Given that a flashlight has lasted more than 100 hours, what is the probability that it was a Type 2 Flashlight?