National University of Singapore

STATISTICS ST2334

1. TRUE/FALSE
Consider an experiment of rolling two six-faced regular FAIR dice. Suppose that the
problem of interest is “the numbers that show on the top faces”.
If the dice are not distinguishable, then the sample space S contains 36 elements.
• TRUE
• FALSE
2. FILL IN THE BLANK
Suppose we will choose THREE numbers from 1, 3, 5, 76, 125, 876, 987, and 1235, with
each number being chosen at most once, to fll in the three boxes below such that the
numbers are arranged in increasing order from left to right. For example, if we choose
the numbers 987, 125, and 1, we shall put “1, 125, and 987” in the boxes from left to
right. How many different ways do we have to fll in the boxes?
ANSWER: . (Leave your answer in numerical form.)
3. FILL IN THE BLANK
A group of 8 friends A,B,C,D,E,F,G,H go to a restaurant. Due to safe-distancing measures, the group needs to split up into two groups of 4. How many ways are there to split
the group such that A and B are together but away from C?
ANSWER: . (Leave your answer in numerical form.)
4. TRUE/FALSE
P(A ∪ B ∪C) = 1 - P(A′|B′ ∩C′)P(B′|C′)P(C′).
• TRUE
• FALSE
5. FILL IN THE BLANK
Find P(B ∩ A), if
P(A′) = 1/2, P(B) = 3/8 and P(B′|A) = 3/4.
ANSWER: . (Round your answer to 3 decimal points, if necessary.)
6. MULTIPLE CHOICE: CHOOSE ONE ANSWER ONLY
Suppose A and B are two events where P(A) = 0.4 and P(A∩ B) = 0.2. What is P(A|B)?
(a) 0.4
(b) 0.5
(c) Insuffcient information to determine
(d) None of the other options