Correct computations.
17. QUESTION: A certain person considers that he can drink and drive: usually he believes he has a negligible chance of being involved in an accident, whereas he believes that if he drinks two pints of beer, his chance of being involved in an accident on the way home is only one in five hundred. Assuming that he drives home from the same pub every night, having drunk two pints of beer, what is the chance that he is involved in at least one accident in one year? Are there any assumptions that you make in answering the question?6. QUESTION: Not all dice are fair. In order to describe an unfair die properly, we must specify the probability for each of the six possible outcomes. The following table gives answers for each of 4 different dice. Probabilities Outcome Die 1 Die 2 Die 3 Die 4 1/3 1/6 1/7 1/3 0 1/6 1/7 1/3 1/6 1/6 1/7 -1/6 0 1/6 1/7 -1/6 1/6 1/6 1/7 1/3 1/3 1/7 2/7 1/3 2 described die, explain why the probabilities are invalid.The height of a randomly selected man from a population is normal with at = 178cm and o = 8cm. What proportion of men from this population are over 185cm tall? There are 2.54cm to an inch. What is their height distribution in inches? The heights of the women in this population are normal with = 165 cm and o = 7cm. What proportion of the women are taller than half of the men?13. QUESTION: An examination consists of multiple-choice questions, each having five possible answers. Suppose you are a student taking the exam. and that you reckon you have probability 0.75 of knowing the answer wo any question that may be asked and that, if you do not know, you intend to guess an answer with probability 1/5 of being correct. What is the probability you will give the correct answer to a question?9. QUESTION: You play draughts against an opponent who is your equal. Which of the following is more likely: (a) winning three games out of four or winning five out of eight; (b) winning at least three out of four or at least five out of eight?39. QUESTION: Find the probability that none of the three bulbs in a set of traffic lights will have to be replaced during the first 1200 hours of operation if the lifetime X of a bulb (in thousands of hours) is a random variable with probability density function f(r) = 60.25 - (r - 1.5) ] when Is r's 2 and f(r) = 0 otherwise. You should assume that the lifetimes of different bulbs are independent.3. QUESTION: A bag contains fifteen balls distinguishable only by their colours; ten are blue and five are red. I reach into the bag with both hands and pull out two balls (one with each hand) and record their colours. (a) What is the random phenomenon? (b) What is the sample space? (c) Express the event that the ball in my left hand is red as a subset of the sample space.10. QUESTION: Count the number of distinct ways of putting 3 balls into 4 boxes when: MB all boxes and balls are distinguishable; BE the boxes are different but the balls are indentical; FD the balls are identical, the boxes are different but hold at most a single ball. See if you can do the counting when there are m balls and n boxes.15. QUESTION: I have in my pocket ten coins. Nine of them are ordinary coins with equal chances of coming up bead and tail when towed and the tenth has two heads. {a} IfI take one of the coins at random from my pocket, what is the probability that it is the coin with two heads ? {b} IfI tom the coin and it comes up heads, what is the probability that it is the coin with two heads 9 {:2} III tom the coin one further time and it comes up tails, what is the probability that it is one of the nine ordinary coins
