#1
If two events are independent, what is the probability of both events occurring?
The product of their probabilities
ExplanationMultiplying the individual probabilities of the events gives the joint probability in case of independence.
#2
What is the probability of drawing an ace from a standard deck of 52 playing cards?
1/13
ExplanationThere are 4 aces in a standard deck of 52 cards.
#3
If two events are mutually exclusive, what is the probability of both events occurring?
The difference of their probabilities
ExplanationMutually exclusive events cannot occur together, so the probability of both happening is 0.
#4
What is the probability of selecting a black card from a standard deck of 52 playing cards?
26/52
ExplanationHalf of the deck consists of black cards.
#5
If two events are independent, what is the probability of neither event occurring?
The quotient of their probabilities
ExplanationThe probability of neither event occurring is the complement of the probability of either event occurring, thus it's obtained by subtracting the sum of their probabilities from 1.
#6
What is the formula for the probability of event A given event B, denoted as P(A|B), if A and B are independent events?
P(A) * P(B)
ExplanationThe probability of A given B, if both events are independent, is the product of the probabilities of A and B.
#7
In a standard deck of 52 playing cards, what is the probability of drawing a red card and then drawing a black card if the cards are drawn without replacement?
26/51
ExplanationAfter drawing a red card, there are 26 black cards remaining out of 51 total cards.
#8
Two events A and B are said to be independent if:
P(A ∩ B) = P(A) * P(B)
ExplanationIf the probability of both events happening together equals the product of their individual probabilities, they are independent.
#9
What is the complement rule in probability?
The probability of an event not occurring is 1 minus the probability of the event occurring
ExplanationThe complement of an event is the probability of it not happening, calculated as 1 minus the probability of the event happening.
#10
If the probability of event A is 0.4 and the probability of event B is 0.3, what is the probability of either event A or event B occurring?
0.7
ExplanationThe probability of either event A or event B occurring is the sum of their individual probabilities.
#11
In a group of 20 students, 12 are boys and 8 are girls. If a student is selected at random, what is the probability that the student is a girl or a boy?
1
ExplanationEvery student must be either a boy or a girl, so the probability of selecting one is guaranteed.
#12
If the probability of event A is 0.6 and the probability of event B is 0.5, what is the probability of both event A and event B occurring if A and B are independent?
0.1
ExplanationSince A and B are independent, their joint probability is the product of their individual probabilities.
#13
What is the formula for conditional probability P(A|B) when A and B are independent events?
P(A|B) = P(A)
ExplanationIf events A and B are independent, the probability of A given B is simply the probability of A.
#14
If the probability of event A is 0.3 and the probability of event B is 0.6, and A and B are mutually exclusive, what is the probability of either event A or event B occurring?
0.9
ExplanationMutually exclusive events cannot occur together, so the probability of either event A or event B happening is the sum of their individual probabilities.
#15
In a group of 30 students, 18 are studying Math, and 12 are studying Physics. If 8 students are studying both Math and Physics, what is the probability that a randomly chosen student is studying at least one of the two subjects?
3/5
ExplanationThere are 22 students studying at least one of the two subjects out of 30 total students.