National University of Singapore
Department of Statistics and Applied Probability
(2019/20) Semester 1 ST2334 Probability and Statistics Tutorial 1
1. NUS library has five copies of a certain textbook on reserve. Two copies (1 and 2) are first
edition, and the other three (3, 4 and 5) are second edition. A student examines these books
one at a time in random order, stopping only when a second edition has been selected. Books
that he examines will not be examined again. One possible outcome is 5, and another is 213.
(a) List the outcomes in the sample space S.
(b) Let Adenote the event that exactly one book must be examined. List the outcomes in A.
(c) Let Bbe the event that book 5 is the one selected. List the outcomes in B.
(d) Let Cbe the event that book 1 is not examined. List the outcomes in C.
(e) Are events Aand Bmutually exclusive events? Explain.
2. Suppose a number is chosen randomly from the set of ten numbers ranging from one to ten.
Let Abe the event that an even number is drawn, Bthe event that an odd number is drawn,
Cthe event that the number drawn is greater than one but less than six, and Dthe event that
the number drawn is either 1,6 or 7. List the outcomes of the following events:
(a) Aor C;
(b) Aand B;
(c) the complement of C;
(d) A, C and the complement of D.
3. Consider the digits 0,2,4,6,8 and 9. If each digit can be used only once,
(a) how many three-digit numbers can be formed from the digits 0,2,4,6,8 and 9?
(b) how many of these are odd numbers?
(c) how many of these odd numbers are greater than or equal to 620?
4. Four married couples have bought 8 seats in a row for a concert. In how many different ways
can they be seated
(a) with no restrictions?
(b) if each couple is to sit together?
(c) if all the men sit together to the right of all the women?
5. An exam paper consists of seven questions. Candidates are asked to answer five questions. Find
the number of choices of the five questions if
(a) no restriction on the choices;
(b) the first two questions must be answered;
(c) at least one of the first two questions must be answered and
(d) exactly two from the first three questions must be answered.
6. Red Riding Hood lives at point A(0,0) wants to visit her grandmother at point B(13,8), and
Big Bad Wolf lives at Y(10,6). At each step, she can only go east or north along the grid as
shown below.
1
