UCSB PSTAT 109 Statistics for Economics Question- Midterm Quiz

1. Let P be a probability and let A; B; C be any events. Then:

2. Let P be a probability and let A and B be two independent events. Then:

3. Let P be a probability and let A and B be two events. If the random

variable X is defined by X = 1A + 2 1B then

4. In a class, 60% of students have an Apple account, 50% have a Google+

Account and 30% have both.

(a) How many (in percentage) don’t have either?

(b) How many (in percentage) have and Apple account but not a Google+

account?

5. In how many different ways 5 people can sleep in a house with 3 rooms

(one person per room and only 3 people can sleep in the house) ?

6. How many different committees of 3 members can be formed out of a

group of 7 people.

7. Suppose a class contains 60% girls and 40% boys. Suppose that 20% of

the girls have blue eyes and 10 % of the boys have blue eyes. What is the

probability that a randomly chosen student has blue eyes ?

8. Suppose that: the probability of snow is 20%, the probability of traffic

accident is 10%, the conditional probability of an accident given that it

snows is 40%. What is the conditional probability that it snow given that

there is an accident?

9. You flip 8 fair coins. Count the number of sequences with exactly 3 Tails.

10. Write the definition of the variance of a random variable and 3 of its

properties.

11. Let P be a probability and let A be any event in the sample space. Prove

that: P (AC ) = 1 P (A):