Probability problems day 2

1. Compute \({5 \choose k}\) for \(k = 0, 1, 2, 3, 4, 5\).
2. Add up your numbers from (a).
3. Using the multiplication principle, determine how many ways you can pick any number of 5 objects (you don’t care about order).

Imagine rolling a die \(30\) times.

1. What is the probability that you saw exactly five \(1\)’s?

2. What is the probability that you saw each possible value (1, 2, 3, 4, 5, 6) exactly five times each?

3. Repeat (b), but assume that we roll the die \(6n\) times, and saw each value exactly \(n\) times. (You should get used to variables!)

1. A family has five boys and four girls. Assuming that the children were born in a random order where all orders are equally likely, what is the probability that the four girls were born first?

2. If there were only one girl, does the probability that she was born first go up or down compared to (a)? Argue amongst your group, then compute the probability.