COMP 283 UPDATED EXAM SCRIPT QUESTIONS AND SOLUTIONS GRADED A+

COMP 283 UPDATED EXAM SCRIPT QUESTIONS AND
SOLUTIONS GRADED A+
✔✔What is the expected number of rolls of a fair six sided die until one gets a number
larger
than two? - ✔✔3/2

✔✔What is the expected value of the product of two successive rolls of a fair six sided
die? - ✔✔12.25

✔✔Suppose A and B are events, P r{A} = 1/2, P r{B} = 1/2, and P r{A ∩ B} = 1/8. What
is P r{A ∪ B}? - ✔✔7/8

✔✔Suppose A and B are events, P r{A} = 2/3, and P r{B} = 2/3. What is the minimum
possible value of P r{A ∩ B}? - ✔✔1/3

✔✔If 5 balls are placed randomly into 3 bins, what is the expected number of balls in
each
bin? - ✔✔5/3

✔✔Suppose one randomly colors the vertices of a clique K4 with two colors. What is the
probability that all vertices will have the same color? - ✔✔1/8

✔✔T/F: If X is a non-negative random variable then P r{X ≥ 5} ≤ E(X)
5. - ✔✔true

✔✔ aa ∈ {a} - ✔✔false

✔✔ab ∈ {a}* - ✔✔false

✔✔ba ∈ {a}{b} - ✔✔false

✔✔ab ∈ {a} U {b} - ✔✔false

✔✔b ∈ {a} U {b} - ✔✔true

✔✔ab ∈ {a}** U {b}** - ✔✔false

✔✔aa ∈ {a}** U {b}** - ✔✔true

✔✔ab ∈ {a}**{b}** - ✔✔true

✔✔ba ∈ {a}**{b}** - ✔✔false