ISYE 2027 Midterm 1 Questions and Answers(A+ Solution guide)

ISYE 2027 Midterm 1
Intersection A ∩ B - ✔️✔️the set of outcomes that belong to both A and B
occurs if and only if both A and B occur

A: event {Born in the first half of the year}
B: event {Born in a long month}
A ∩ B? - ✔️✔️A ∩ B = {Jan, Mar, May}

Union A ∪ B - ✔️✔️set of outcomes that belongs to either A or B (or both). A ∪ B only
occurs if at least one of the events A and B occurs

A: event {Born in the first half of the year}
B: event {Born in a long month}
A ∪ B? - ✔️✔️A ∪ B = {Jan, Feb, Mar, Apr, May, June, Jul, Aug, Oct, Dec}


Flipping a coin (two possible outcomes). What is the sample space? T - ✔️✔️Sample
space: {Head, Tail}

Flip two coins sequentially. What is the sample space?
EVENT: first flip gives a Head. What is the subset of outcomes? - ✔️✔️{HH, HT, TH,
TT}
Subset: {HH, HT}

Flip a coin until I get a Head. What is the sample space? - ✔️✔️{0, 1, 2,...}
{H, TH, TTH,...}
Both are infinite and countable

Pick a student and ask for his/her birthday month. What is the sample space?
EVENT: He/she is born in the first half of the year. Subset? - ✔️✔️12 months of the
year
Subset: {Jan, Feb, March, Apr, May, June}

Find a bridge and load it with weights until it collapses. What is the sample space? -
✔️✔️All non-negative real numbers


Experiment - ✔️✔️any situation involving some element of uncertainty/randomness,
where different possible outcomes can be identified in advance

Outcome - ✔️✔️each possible thing that can happen as the result of an experiment