WORKSHEET 7
1.
A card is selected at random from a pack consisting of a total of 52 cards, including 4 queens and
4 kings. The card is
not
replaced. A second card is selected. Find the probability that the second
card is a queen, given that the first card is a king.
(A standard deck has a total of 52 cards, including 4 queens and 4 kings as shown in the lecture
notes)
2.
A Statistics class has an enrollment of 300. Out of these, 95 are taking the Actuarial Statistics
major, 120 are Data Science majors, 80 are Financial Math majors and 5 are Undecided. Find the
probability that a student in the class chosen at random is neither an Actuarial Statistics nor a
Data Science major.
3.
A two-digit number is chosen at random. What is the probability that the chosen number is a
multiple of 5?
4.
Next quarter, a student must choose 4 courses among the 20 being offered. In order to complete
his major requirements, at least one of these courses must be from the PSTAT department, which
is offering 5 courses. How many ways can he choose the 4 courses?
(Hint: the answer is NOT
(
5
1
)(
19
3
)
. Consider counting the number of invalid selections).
5.
Three white paint balls, A, B and C, are fired at a target independently. The probability that paint
ball A will hit the target is
0.7, the probability that paint ball B will hit the target is 0.8, and the
probability that paint ball C will hit the target is 0.9.
a.
What is the probability that at least one of them will hit the target?
b.
What is the probability that A will miss, B will hit the target and C will miss the target?
6.
Among 35 students in a class, 17
earned "A" on the midterm, 14 earned "A" on final exam, and
11 did not earn "A" on either exam. What is the probability that a randomly selected student from
this class earned "A" on both exams?
END WORKSHEET 7