Sample Spaces & Events
What is a sample space in probability?
The set of all possible outcomes
What does the union of two events (A∪B) mean in words?
Outcomes that are in A or B or both.
Probabilities are always between what two numbers?
0 and 1
Which sum is most likely when rolling two dice?
7 (6/36 chance, the highest).
Give an example of a certain event. ANY
The sun will rise tomorrow / rolling a number between 1 and 6 on a die.
What is an event in probability?
A subset of the sample space
What does the intersection of two events (A∩B) mean in words?
Outcomes that are in both A and B.
What is the probability of the whole sample space?
1
Everyday life: You and a friend flip coins. What’s the chance at least one comes up heads?
3/4 = 75%
Give an example of an impossible event.
Rolling a 7 on one die / drawing a 15 from a standard deck.
Flipping a coin once: what is the sample space?
{Heads, Tails}
If P(E)=0.4, what is P(E^c)?
0.6 (since complement = 1 – P(E))?
True or False: Probabilities can be negative.
False.
Blackjack: You have 10 + 3, dealer shows 9. Should you hit or stand?
Hit, chances of busting are 5/13 while hitting are 8/13
Which is more likely: rolling a 7 with two dice or rolling a 2?
Rolling a 7 (6/36 vs 1/36).
Rolling one die: how many outcomes are in the sample space?
6 outcomes: {1,2,3,4,5,6}.
In roulette, what does the union of “red” and “even” mean?
All numbers that are red, or even, or both
What is the Complement Rule in words?
The probability of “not E” is 1 – P(E)
In UNO, if you randomly draw a card from a full deck, what is the probability it’s red? (lets say theres only 100 cards in a uno deck and 4 colors with equal amounts for each color)
What is 25%? (since there are 25 red cards out of 100 total).
Probability of rolling snake eyes (double ones) with two dice?
1/36 ≈ 2.8%.
Rolling two dice: how many outcomes are in the sample space?
36 outcomes (since 6 × 6).
State the Addition Rule formula for P(E∪F)
P(E)+P(F)–P(E∩F)
What is the Inclusion–Exclusion Principle used for?
Calculating probabilities with 3 or more events.
If a coin is flipped 5 times, what is the probability it lands on heads every time?
1/32 about 3.1%?
Why is rolling a 13 with two dice impossible?
The maximum sum of two dice is 12.