Jenn figures she has a 70% chance of passing math and an 80% chance of passing history. a. What is the probability that she passes math and history? What assumption did you have to make to answer this question? (1 mark) b. What is the probability that she will pass one but not both? Note: There are two different ways that this can happen. Find the probability of both. (2 marks) C. What is the possibility that she will pass neither? (1 mark) d. Is there any other possible outcome for Jenn, other than those listed in a, b and c? What should the three probabilities in a, b and c add up to? Do your probabilities add up correctly? (1 mark) 6. Suppose that Jenn also studies English and has a 90% chance of passing it. Draw a tree diagram that shows all the possible pass/fail combinations for Jenn in those three subjects. Calculate the total probabilities for each of the branches in your tree. (2 marks) 7. Decide whether the following scenarios are permutations or combinations and then answer each question. The neighbourhood pizzeria has a special on large pizzas with four toppings. Last month Josh claimed he had eaten at least one slice from every kind of pizza that they could make on that special. If they have 15 toppings to pick from, do you believe Josh's claim? Explain. (2 marks) b. How many ways can you pick a committee of three people from a group of ten? How many ways could you pick a committee of seven from that group of ten? What do you notice about these two answers? Can you explain why this happens? (2 marks) c. How many different "words" can we make with the word "Newfoundland" if we must use every letter each time? Keep in mind that a "word" does not have to make sense or be in any dictionary-it only must be a unique combination of the 12 letters. (1 mark) d. There are 35 players dressed for tonight's hockey game. In how many ways can we pick the first, second and third stars of the game? (1 mark) 8. The probability of picking the person you want at random from the entire population of New York City is one out of eight million. Compare this to the probability of picking the winning 6/49 lottery number where you must pick 6 numbers out of 49 correctly. How good are your chances of winning the lottery? (2 marks) 9. Use your knowledge of combinations, Pascal's Triangle and the Binomial Theorem to expand completely each of the following expressions: (4 marks) a (3x + 1): b. (2x - 5): 10. What is now five of Pascal's Triangle? Show where these numbers appear in your answer to question 9 b. (1 mark)