1. We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance team of 5 has to by picked randomly from the crew of 7 boys and 3 girls. What is the probability that less than 4 boys are picked in this team of 5?
2. Consider the rolling of 2 six-sided fair dice, find the conditional probability P(first dice =3 | sum of two dice = 7). Are these two events independent?