Читать книгу Probability - Robert P. Dobrow - Страница 42

1 1.1 Your friend was sick and unable to make today's class. Explain to your friend, using your own words, the meaning of the terms (i) random experiment, (ii) sample space, and (iii) event.For the following problems 1.2–1.5, identify (i) the random experiment, (ii) the sample space, and (iii) the event of interest.

2 1.2 Roll four dice. Consider the probability of getting all fives.

3 1.3 A pizza shop offers three toppings: pineapple, peppers, and pepperoni. A pizza can have 0, 1, 2, or 3 toppings. Consider the probability that a random customer asks for two toppings.

4 1.4 Bored one day, you decide to play the video game Angry Birds until you win. Every time you lose, you start over. Consider the probability that you win in less than 1000 tries.

5 1.5 In Julia's garden, there is a 3% chance that a tomato will be bad. Julia harvests 100 tomatoes and wants to know the probability that at most five tomatoes are bad.

6 1.6 In two dice rolls, let be the outcome of the first die, and the outcome of the second die. Then is the sum of the two dice. Describe the following events in terms of simple outcomes of the random experiment: (Example solution: .)....

7 1.7 A bag contains red and blue balls. You reach into the bag and take balls. Let be the number of red balls you take. Let be the number of blue balls. Express the following events in terms of and , assuming valid values for , , and :You pick no red balls. (Example solution: .)You pick one red and two blue balls.You pick four balls.You pick twice as many red balls as blue balls.You pick at least two red balls.

8 1.8 A couple plans to continue having children until they have a girl or until they have six children, whichever comes first. Describe an appropriate sample space for this random experiment.