Transcript assignment 1

Home assignment 1
1.
For what number of students n the probability that none of them have a birthday
on the same day equals 0.2?
2.
A card is drawn at random from an ordinary deck of 52 playing cards. Describe
the sample space if consideration of color (red or black) (a) is not, (b) is, taken in
the account. Try the same if distinction between the “faces” and the “digits” (a) is
not, (b) is, taken in the account.
3.
Consider the set of 20 cards representing 20 amino acids (aa): {A, I, L, M, F, P,
W, V, N, C, Q, G, S, T, Y, R, H, K, D, E}*. It is known that some of the aa are
usually charged while some others are neutral. Some of the aa are hydrophobic
and some are hydrophilic. The card is drawn at random from this set.
(a)
Describe the events: C= “selected aa is typically charged”; N= “selected aa is
neutral”; B = “aa is hydrophobic”; L= “aa is hydrophilic”.
(b) Find their probabilities.
* Use the following two slides. You can learn more from the “Protein Sequence and
Structure Analysis” class offered in our department
Polar (hydrophilic) amino acids
Positively
charged
-helix
favoring
Negatively
charged
-sheet favoring
Small
Hydrophobic amino acids
Helix Favoring
-sheet favoring
Helix and
sheet breaking
Small
Big
4.
Referring to the previous problem. , let H=“hydrophobic AA is is
drawn" and Q=“a charged AA is drawn". Describe the events (a)
BUC, (b) BC,
(c) BCc (d) Bc Cc (d) (BC) (BCc)
5.
Items being produced on an assembly line can be good (G) or bad
(B). Show the sample space for the next 3 items produced by the
assembly line.
6.
A die is loaded in such a way that the probability of each face
turning up is inversely proportional to the number of dots on that face
(for instance, six is three times less probable as two). What is the
probability of getting an odd number in one throw?
7. In a sample space is it possible to have
1
1
1
P( A)  , P( A  B)  , P( B)  .
2
3
4
Justify your answer.
8. Through a pair of fair dice. What is the probability that the dice show
different numbers?
9. Choose at random one card from the deck of 52 cards.
Let A = “the selected card is a heart” and B= “the selected card is a face
card”. Find the probability P(AUB)*.
* We will be using sometime “U” to denote the union.