Definitions
Define mutually exclusive events.
Two events that can never happen at the same time
What is the probability of rolling a 3 on a fair six-sided die?
1/6
What is the probability of flipping a coin and rolling a die, getting heads and a 4?
0.5 X 1/6 = 0.083
What is the addition rule for probabilities?
P(A or B)=P(A)+P(B)- P(A and B)
What is the probability of drawing a red card from a standard deck of 52 playing cards?
1/2
What is the probability of drawing two cards from a deck without replacement, and both being aces?
1/221
A box contains 4 defective and 6 non-defective items. If one item is selected, what is the probability that it is defective given that it is from the first batch?
0.4
What is the sample space of flipping a coin three times
S={HHH,HHT,HTH,HTT,TTT,TTH,THT,THH}
Give an example of two mutually exclusive events in a deck of cards.
ex:drawing a heart and a club card
If a die is rolled, what is the probability of rolling a number greater than 4?
2/6=1/3
If two dice are rolled, what is the probability of getting a total of 7?
1/6
If a bag contains 3 red balls and 2 blue balls, what is the probability of drawing a blue ball given that a red ball was drawn first and not replaced?
2/4 or 1/2
If the odds in favor of an event are 3 to 2, what is the probability of that event occurring?
3/5
In a class of 30 students, 18 are girls. What is the probability of randomly selecting a boy from the class?
12/30 = 4/10= 2/5
Calculate the probability of drawing a heart or a queen from a standard deck of cards.
16/52 = 4/13
In a deck of cards, what is the probability of drawing a heart given that the card drawn is a face card?
1/4
X 0 0.5 0.5
P(X) 0.2 -0.2 1
the probability distribution above is a valid one? why?
No, because no probability can be negative, although they add up to 1
If two events are not mutually exclusive, how do you calculate the probability of either event occurring?
P(A∪B)=P(A)+P(B)−P(A∩B)
If you roll two dice, what is the probability that at least one die shows a 6?
11/36
If 60% of students study for the exam and 80% of those who study pass, what is the probability that a student who studies passes?
80%