Math 419 : Exam P
REVIEW
Probability
Problem Set 1
Math 419 : Exam P
Probability
Problem Set 1
Math 419 : Exam P
Probability
Problem Set 1
1. A medical study needs to enroll 268 patients with heart disease, 268 patients with diabetes, and 268
patients with high cholesterol. They also need 68 patients with heart disease only, 68 patients with
diabetes only, and 68 patients with high cholesterol only. Furthermore, they must have 84 with all
three conditions. If they have 155 patients enrolled without any of these conditions, how many
patients do they need to enroll in their study?
2. If five dice are rolled, what is the probability of obtaining three identical odd numbers and two
identical even numbers?
Math 419 : Exam P
Probability
Problem Set 1
3. Three fair dice are rolled and X is the smallest number of the three values resulting (if more than one
value is the smallest one, we still use that value). Find P (X = 3) .
4. Let A be the event a rolled die gets less than 5, B be the event a rolled die gets less than 4, and C be
the event a rolled die gets a 6. Given P(A) = 0.3, P(B) = 0.1, and P(C) = 0.7, what is
P(A Ç B) + P(A Ç C) + P(B Ç C) ?
Math 419 : Exam P
Probability
Problem Set 1
5. We have two identical fair dice. They have one dot on 2 sides and 2 dots on the other 4 sides. Find
the probability that, when the dice are rolled, the sum of the upturned faces is not less than three.
6. A portfolio has three types of investments consisting of 5 high risk, 3 moderate risk, and 2 low risk.
Four investments from the portfolio are selected at random. Calculate the probability that at least one
investment of each type is selected.