stat310
Homework 1
Due Jan 21, in class. Your assignment should be neatly written, stapled and have your name in the top-right corner of the first page. The homework is graded out 10, with the possibility of 2 points of extra credit, and a 1 point penalty for poor presentation. Partial credit will be given for working.
- (3 points) Do you think the message from the Governor was deliberate or accidental. Justify your answer. Which of the probability models we discussed in class do you think is most appropriate? How could we do better?
- 2.2.2. (1 point) A coin is tossed three times. Define an appropriate sample space for the following cases
- The outcome of each individual coin toss is of interest.
- Only the number of trials is of interest
- 2.2.16 (a), (b) (1 point). If A and B are mutually exclusive events, $$P(A) = 0.17$$ and $$P(B) = 0.46$$, find:
- $$P(A \cup B)$$
- $$P(A^c)$$
- 2.2.3. (2 points) A pair of six-sided balanced dice are rolled. What are the probabilities of getting the sum of the face values as follows:
- 8
- 6 or 9
- 3, 8, or 12
- Not an even number
- 2.3.4. (1) Insulin, a peptide hormone, is built from 51 amino acid residues. There are twenty standard amino acids. How many other possible 51 amino acid proteins are there?
- 2.3.5 (1) An exmination is designed where the students are required to answer any 20 questions from a group of 25 questions. How many different ways can a student choose the 20 questions?
- 2.3.17 (1) Five white and four black balls are arranged in a row. What is the probability that the end balls are of different colours?
Extra credit (2 points): Using the axioms of probability, show that:
- $$P(A^c) = 1 - P(A)$$
- If $$A \subset B$$ then $$P(A) \leq P(B)$$
- $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$