Download HWTP- test practice

HWTP
1.
How many distinguishable arrangements are there of the letters in the word
PROBABILITY?
2.
A and B are special dice. The faces of A are 2,2,5,5,5,5 and the faces of B are
3,3,3,6,6,6. The two die are rolled. What is the probability that the number
showing on die B is greater than the number showing on die A?
Hint: try presenting the event F= “the number showing on die B is greater than
the number showing on die A” as a combination of the elementary events using
“either or” and “and” operations.
3.
The integers 1,2,3,4 are randomly permuted. What is the probability that 4 is
to the left of 2?
4. A box contains 8 red, 3 white and 9 blue balls. Three balls are to be drawn without
replacement. What is the probability that more blues than whites are drawn?
Hint: Present this event as a union of simpler events (use “B” (for blue), “W” and “R”
letters. Do not forget that BRR, for example, also satisfies the requirement.
5. A production lot has has 100 units of which 25 are known to be defective. A random
sample of 4 units is chosen without replacement. What is the probability that the sample
will contain no more than 2 defective units.
Hint: (a) Notice that “At most 2 defective” = “0 defective” + “1 defective” + “2
defective”.
6. The combinatorics of disulfide bond formation.
A protein may contain several cysteines, which may pair together
to form disulfide bonds as shown in Figure 1.17.
If there is an even number n of cysteines, n/2 disulfide
bonds can form. How many different disulfide pairing arrangements
are possible?