Easy
What is conditional probability?
A. The probability of two events occurring together
B. The probability of an event occurring given that another event has already occurred
C. The probability of an event happening independently
D. The probability of at least one event happening
B. The probability of an event occurring given that another event has already occurred
If P(A∩B) = 0.2 and P(B) = 0.5, find P(A∣B).
A. 0.25
B. 0.4
C. 0.5
D. 0.7
B. 0.4
A deck has 10 red and 6 black cards. If a red card is drawn first, what is the probability the second is red?
A. 10/16
B. 9/15
C. 10/15
D. 6/15
B. 9/15
What does P(A∣B) mean?
A. Probability of event B given event A
B. Probability of event A happening independently
C. Probability of event A given event B
D. Probability of both events A and B
C. Probability of event A given event B
If 15 students are athletes and 6 of them are honor students, what is P(Honor∣Athlete)?
A. 6/15
B. 15/6
C. 2/3
D. 1/3
A. 6/15
A jar contains 7 green and 3 yellow marbles. If a green marble is drawn first without replacement, what is P(Yellow∣Green)?
A. 1/4
B. 1/3
C. 3/10
D. 3/9
B. 1/3
When are events considered dependent?
A. When the occurrence of one event affects the probability of another
B. When events cannot occur together
C. When events are mutually exclusive
D. When the probability of one event is zero
A. When the occurrence of one event affects the probability of another
If P(A) = 0.6, P(B) = 0.5, and P(A∩B) = 0.3, find P(A∣B).
A. 0.3
B. 0.5
C. 0.6
D. 0.9
C. 0.6
In a survey, 30 students like Math. 12 of them are in Section A. Find P(SectionA∣LikesMath).
A. 12/30
B. 12/12
C. 1/3
D. 2/3
A. 12/30
Why must P(B) ≠ 0 in conditional probability?
A. Because B must always happen
B. Because we cannot divide by zero
C. Because A depends on B
D. Because P(A∩B) = 0
B. Because we cannot divide by zero
A bag has 5 red and 5 blue balls. If one red ball is drawn first without replacement, how many balls remain?
A. 10
B. 9
C. 5
D. 4
B. 9
In a class of 60, 25 are athletes. Among athletes, 10 are honor students. Find P(Honor∣Athlete).
A. 10/60
B. 2/5
C. 1/2
D. 10/25
B. 2/5
What is the formula for conditional probability?
A. P(A∣B) = P(A) × P(B)
B. P(A∣B) = P(A∪B)/P(B)
C. P(A∣B) = P(A∩B)/P(B)
D. P(A∣B) = P(B∣A) × P(A)
C. P(A∣B) = P(A∩B)/P(B)
A box has 6 apples and 4 oranges. If the first fruit drawn is an apple, what is the probability the second is orange?
A. 4/10
B. 4/9
C. 6/10
D. 6/9
B. 4/9
Out of 50 students, 20 play basketball. Among them, 8 are girls. Find P(Girl∣Basketball).
A. 8/50
B. 2/5
C. 1/4
D. 8/20
B. 2/5