Språkstatistik HT97:09

Exercise class 3

Deadline

These exercises are supposed to be handed in on Monday September 29.

Exercises

1. A box contains four blue cards and one yellow card. We make two draws without replacement from the box. What is the chance that the second card is yellow if we do not look at the color of the first one? And what is the chance that the second card is yellow if we know that the first card was blue?

2. We will try to complete the sentence "The current year is . . . ." by filling in the gaps with cards we obtain by making four draws without replacement from a standard deck of 52 cards. What is the chance of getting the sentence right?

3. We throw two dice. What is the probability that neither of them is a five or a six?

4. In how many different orders can one arrange a set of three red cards, two white cards and four blue cards?

5. What is the probability of obtaining a total of fourteen points when throwing four dice? If you find that you have to perform too many computations you may compute the probability of obtaining a total of fourteen points when throwing three dice.

6. We flip a coin seven times. What is the probability of obtaining exactly three heads? And what is the probability of obtaining exactly four heads?

7. A box contains two white marbles and two black ones. We make five draws from the box. When we draw a white marble we put back a black marble in the box. When we draw a black marble we put back a white one. We want to know what the probability is of drawing exactly three white marbles. Would it be correct to use the binomial formula for computing this? Motivate your answer.

8. Is it possible that two events are mutually exclusive while at the same time being independent of each other? Motivate your answer.

9. Each week you participate in a lottery which offers a 1 in a 1000 chance of winning the main price. How many weeks will you need to participate to have more than 50% chance of winning this price?

10. A statistics class with twelve female students and eight male students is tested. Six female students and one male student obtain the maximal score. What is the probability of this event happening again if we assume that the probability of obtaining the maximal score for the test does not change and is the same for all students? You may assume that the number of female students with a maximal score is independent of the number of male students with a maximal score.

Each exercise is worth 1 point.

Related Exercises

If you want to make extra exercises you can try the following optional exercises from the second edition of the book:

probability: 13C1, 13D5, 13D6, 13E1, 13E3, 14B9, 14B10, 14C2.
binomial formula: 15A5, 15R6, 15R7.

A code like 13C1 points to the second exercise of section C from chapter 1. R stands for review exercise. The answers to these exercises can be found in the final part of the book.