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

Review Midterm Exam: PSTAT109, Feb., 2014.

There is only one correct answer in each multiple choice questions #1,#2,#3.

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

(a)P(A\B\C) =P(A)P(B)P(C)

(b)P(A[B[C) =P(A) +P(B) +P(C)

(c)P(A) =P(A\C) +P(A\CC)

(d)P(A[B[C) = 1

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

(a)P(A[B) =P(A) +P(B)

(b)P(A\B) =P(A[B)????P(A)

(c)P(AC\B) =P(AC)P(B)

(d) none of the previous answers

3. LetPbe a probability and letAandBbe two events. If the random variableXis de.ned byX=1A+ 2_1Bthen

(a)E[X] =P(A\B)

(b)X_1A\B= 3_1A\B

(c)E[X] =P(A) +P(B)

(d) none of the previous answers

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 di¤erent 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 di¤erent 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 a tra¢ c 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 .ip 8 fair coins. Count the number of sequences with exactly 3 Tails.

10. Write the de.nition of the variance of a random variable and 3 of its properties.

11. LetPbe a probability and letAbe any event in the sample space. Prove that: P(AC) = 1????P(A):