Basic Probability
What is the probability of rolling a 3 on a fair six-sided die?
1/6
there is only one side with with a 3 on a 6 sided die
Define Probability
The measure of how likely an event is to occur.
What is the rule for the probability of two events A and B if they are mutually exclusive?
P(A or B) = P(A) + P(B)
You roll two dice. What is the probability of getting a total 7?
6/36
there are 36 possible outcomes and 6 outcomes of getting a 7
What is the probability of selecting a red marble if there are 5 red marbles and 15 total marbles in a bag?
5/15 -> 1/3
What is an independent event?
Two events where the outcome of one does not affect the outcome of the other.
What is the formula for the probability of the intersection of two independent events A and B?
P(A and B) = P(A) x P(B)
A bag contains 3 red balls and 2 blue balls. One ball is chosen at random. What is the probability of selecting a red ball?
3/5
If you flip a coin three times, what is the probability of getting exactly two heads?
3 outcomes out of 8 -> 3/8
Define Mutually Exclusive Events.
Events that cannot happen at the same time.
What is the addition rule in probability when events are not mutually exclusive?
Probability of A or B = P(A) + P(B) - P(A and B)
If P(A) = 0.4 and P(B) = 0.5, and A and B are independent, find P(A and B)
0.2
P(A and B)=0.4 x 0.5
P(A and B)=0.2
20%
A deck has 52 cards. What is the probability of drawing a king or queen?
8/52 ->2/13
What is the expected outcome in probability?
The long-term average outcome of a random event.
What is the rule for conditional probability?
The probability of A given B is P(A and B)/P(B)
A bag contains 4 red and 6 blue balls. Two balls are drawn. What is the probability both are red?
2/15
In a class of 40 students,25 have completed their homework. What is the probability that a randomly selected student has not completed their homework?
15/40 -> 3/8
Define conditional probability
The probability of one event occurring given that another event has already occurred.
What is the probability rule when events A and B are mutually exclusive?
If A and B are mutually exclusive, P(A and B) is 0, so P(A or B) = P(A)+P(B)
A class has 12 girls and 8 boys. Five of the girls and three of the boys wear glasses. If A student who wears glasses is chosen at random, what is the probability that the student is a girl?
5/8
8 total students who wear glasses and 5 of them are girls.