Språkstatistik HT96:09

Class:   09
Date:    960918
Topic:   Exercise class 3

Exercise class 3

These exercises are supposed to be handed in on Monday September 23. Please give a motivation for all your answers.

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

2. We will try to complete the sentence "The ........ of Sweden has ........ children." by filling in the gaps with the cards we obtain from making two draws with replacement from a 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 one or a two?

4. A deck of cards contains 52 cards. We shuffle the deck. What is the probability that the top card is neither an ace nor a king?

5. Is it possible that two events are independent of each other and at the same time mutually exclusive?

6. What is the probability of obtaining a total of seven points when throwing four dice?

7. In how many ways can one arrange a set of two red cards and three green cards? And in how many ways can one arrange a set of two red cards, three green cards and four yellow cards?

8. We flip a coin six times. What is the probability of obtaining exactly two heads?

9. A box contains four red marbles and six green ones. We make five draws without replacement. Suppose we want to know what the probability is of obtaining exactly three red marbles. Would it be correct to use the binomial formula for computing this?

10. A statistics class with fourteen female students and six male students is tested. Six female students and one male student obtain a maximal score. What is the probability of this event if we assume that the probability of obtaining a maximal score for the test 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.