Question

Exercise 4.8.24 Let \(\Omega\) have n elements. How many partitions are there of \(\Omega\) into exactly k sets, for each \(k \in \{1, \dots, n\}\)? Conditional Probability, Independence, and Bayes' Theorem \(\cdot\) 155 Exercise 4.8.25 Let's revisit the previous exercise. Assume all possible partitions of \(\Omega\) are equally likely. If n = 4 what is the probability that all sets in the partition have the same number of elements? Can you answer this for general n? Exercise 4.8.26 We flip a coin that is heads with probability .2 and tails with probability .8. We then roll two fair (and independent) die if the coin comes up heads, or roll three fair die if it comes up tails. What is the probability the sum of the dice is 3?

          Exercise 4.8.24
Let \(\Omega\) have n elements. How many partitions are there of \(\Omega\) into
exactly k sets, for each \(k \in \{1, \dots, n\}\)?
Conditional Probability, Independence, and Bayes' Theorem  \(\cdot\) 155
Exercise 4.8.25
Let's revisit the previous exercise. Assume all possible partitions of
\(\Omega\) are equally likely. If n = 4 what is the probability that all sets in the partition have
the same number of elements? Can you answer this for general n?
Exercise 4.8.26
We flip a coin that is heads with probability .2 and tails with
probability .8. We then roll two fair (and independent) die if the coin comes up heads,
or roll three fair die if it comes up tails. What is the probability the sum of the dice is 3?

Exercise 4.8.24
Let Ω have n elements. How many partitions are there of Ω into
exactly k sets, for each k ∈{1, …, n}?
Conditional Probability, Independence, and Bayes' Theorem · 155
Exercise 4.8.25
Let's revisit the previous exercise. Assume all possible partitions of
Ω are equally likely. If n = 4 what is the probability that all sets in the partition have
the same number of elements? Can you answer this for general n?
Exercise 4.8.26
We flip a coin that is heads with probability .2 and tails with
probability .8. We then roll two fair (and independent) die if the coin comes up heads,
or roll three fair die if it comes up tails. What is the probability the sum of the dice is 3?

Added by Josefina K.

Question

Please give Ace some feedback