Q. A bag contains 3 red and 2 blue balls. If one ball is drawn at random, what is the probability that it is red given that it is not blue?
A.1/2
B.3/5
C.2/5
D.3/4
Solution
The total number of balls that are not blue is 3 (red). The probability of drawing a red ball given that it is not blue is 3/5.
Correct Answer: B — 3/5
Q. A bag contains 3 red balls and 2 blue balls. If one ball is drawn at random, what is the probability that it is red?
A.1/5
B.2/5
C.3/5
D.4/5
Solution
The total number of balls is 3 + 2 = 5. The probability of drawing a red ball is 3/5.
Correct Answer: C — 3/5
Q. A box contains 10 balls, 4 of which are red and 6 are blue. If one ball is drawn at random, what is the probability that it is not blue?
A.2/5
B.3/5
C.4/10
D.1/5
Solution
The probability of not drawing a blue ball = Number of red balls / Total balls = 4/10 = 2/5.
Correct Answer: A — 2/5
Q. A box contains 10 balls, 4 of which are red and 6 are blue. If one ball is drawn, what is the probability that it is blue?
A.2/5
B.3/5
C.4/10
D.6/10
Solution
The probability of drawing a blue ball is 6/10 = 3/5.
Correct Answer: B — 3/5
Q. A box contains 10 balls, 4 of which are white and the rest are black. If one ball is drawn at random, what is the probability that it is not white?
A.2/5
B.3/5
C.4/5
D.1/5
Solution
The total number of balls is 10. The number of non-white balls is 10 - 4 = 6. Thus, the probability of drawing a non-white ball is 6/10 = 3/5.
Correct Answer: B — 3/5
Q. A box contains 10 balls, 4 red and 6 green. If one ball is drawn at random, what is the probability that it is green given that it is not red?
A.1/2
B.3/5
C.2/5
D.4/5
Solution
If the ball is not red, it must be green. Therefore, P(Green | Not Red) = 1.
Correct Answer: B — 3/5
Q. A box contains 4 red, 3 green, and 2 blue balls. If a ball is drawn and it is green, what is the probability that the next ball drawn is red?
A.4/9
B.2/9
C.1/3
D.1/4
Solution
After drawing a green ball, there are 4 red, 2 green, and 2 blue balls left. The probability of drawing a red ball next is 4/8 = 1/2.
Correct Answer: A — 4/9
Q. A box contains 4 red, 3 green, and 5 blue balls. If a ball is drawn and it is blue, what is the probability that the next ball drawn is red?
A.4/11
B.3/11
C.5/11
D.1/3
Solution
After drawing a blue ball, there are 4 red, 3 green, and 4 blue left. The probability of drawing a red ball next is 4/11.
Correct Answer: A — 4/11
Q. A box contains 4 white and 6 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is also black?
A.1/2
B.1/3
C.1/5
D.2/5
Solution
After drawing one black ball, there are 5 black and 4 white balls left. The probability of drawing another black ball is 5/9.
Correct Answer: D — 2/5
Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is white given that it is not black?
A.2/5
B.1/5
C.1/2
D.1/3
Solution
If the ball is not black, it must be white. Therefore, P(White | Not Black) = 1.
Correct Answer: A — 2/5
Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
A.2/5
B.3/5
C.4/5
D.1/5
Solution
The total number of balls is 10. The number of favorable outcomes (black balls) is 6. The probability that the ball is black given that it is not white is P(Black | Not White) = 6/6 = 1.
Correct Answer: C — 4/5
Q. A box contains 5 red and 3 blue balls. What is the probability of drawing a red ball?
A.5/8
B.3/8
C.1/2
D.1/4
Solution
Total balls = 5 + 3 = 8. Probability of red = 5/8.
Correct Answer: A — 5/8
Q. A box contains 5 red and 3 green marbles. If one marble is drawn and it is red, what is the probability that the next marble drawn is green?
A.3/7
B.2/7
C.1/7
D.1/3
Solution
After drawing one red marble, there are 4 red and 3 green marbles left. The probability of drawing a green marble is 3/7.
Correct Answer: A — 3/7
Q. A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
A.1/2
B.1/4
C.1/3
D.1/5
Solution
The total number of balls that are not red is 5 (3 blue + 2 green). The probability that the ball is blue given it is not red is P(Blue | Not Red) = 3/5.
Correct Answer: C — 1/3
Q. A box contains 5 red, 3 green, and 2 blue balls. What is the probability of drawing a green ball?
A.1/5
B.3/10
C.1/3
D.1/2
Solution
Total balls = 10. Probability of green = 3/10.
Correct Answer: B — 3/10
Q. A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn at random, what is the probability that it is green given that it is not red?
A.1/2
B.1/3
C.1/4
D.1/5
Solution
The total number of non-red marbles is 5 (3 green + 2 blue). Therefore, P(Green | Not Red) = 3/5.
Correct Answer: B — 1/3
Q. A box contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is green given that it is not red?
A.1/2
B.1/3
C.1/4
D.1/5
Solution
The total number of non-red marbles is 5 (3 green + 2 blue). The probability that the marble is green given that it is not red is P(Green | Not Red) = 3/5.
Correct Answer: B — 1/3
Q. A box contains 5 red, 3 green, and 2 blue marbles. What is the probability of drawing a green marble given that the marble drawn is not blue?
A.3/10
B.1/3
C.1/5
D.1/2
Solution
The total number of marbles that are not blue is 8 (5 red + 3 green). The probability of drawing a green marble is 3/8.
Correct Answer: A — 3/10
Q. A box contains 5 white and 3 black balls. If a ball is drawn and it is black, what is the probability that the next ball drawn is white?
A.5/8
B.3/8
C.1/2
D.1/3
Solution
After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/7.
Correct Answer: A — 5/8
Q. A box contains 5 white and 3 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is white?
A.5/7
B.3/8
C.5/8
D.1/2
Solution
After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/7.
Correct Answer: A — 5/7
Q. A box contains 5 white and 3 black balls. If one ball is drawn at random, what is the probability that it is not black?
A.3/8
B.5/8
C.1/2
D.7/8
Solution
The probability of not drawing a black ball is the probability of drawing a white ball, which is 5/8.
Correct Answer: B — 5/8
Q. A box contains 5 white and 3 black balls. If two balls are drawn at random, what is the probability that both are white?
A.1/28
B.5/28
C.15/28
D.3/28
Solution
The probability of drawing 2 white balls = (5/8) * (4/7) = 20/56 = 5/14.
Correct Answer: B — 5/28
Q. A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?
A.30 degrees
B.36.87 degrees
C.45 degrees
D.60 degrees
Solution
Using tan(θ) = height/distance, we have tan(θ) = 30/40 = 0.75. Therefore, θ = tan⁻¹(0.75) ≈ 36.87 degrees.
Correct Answer: B — 36.87 degrees
Q. A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?
A.20√3 m
B.40 m
C.30 m
D.10√3 m
Solution
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.
Correct Answer: A — 20√3 m
Q. A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart given that it is a red card?
A.1/2
B.1/4
C.1/3
D.1/13
Solution
There are 26 red cards (hearts and diamonds). The probability of drawing a heart given that it is red is 13/26 = 1/2.
Correct Answer: A — 1/2
Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart given that it is a red card?
A.1/2
B.1/4
C.1/3
D.2/3
Solution
There are 26 red cards (hearts and diamonds). The probability of drawing a heart given that the card is red is 13/26 = 1/2.
Correct Answer: A — 1/2
Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card drawn is a heart?
A.1/4
B.1/13
C.1/52
D.3/13
Solution
There are 13 hearts in a deck of 52 cards. The probability of drawing a heart is 13/52 = 1/4.
Correct Answer: A — 1/4
Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card drawn is a queen?
A.1/13
B.1/52
C.1/26
D.3/52
Solution
There are 4 queens in a deck of 52 cards. Probability = 4/52 = 1/13.
Correct Answer: A — 1/13
Q. A die is rolled. What is the probability of getting a number greater than 4?
A.1/6
B.1/3
C.1/2
D.1/4
Solution
Numbers greater than 4 are 5 and 6. Probability = 2/6 = 1/3.
Correct Answer: B — 1/3
Q. A die is rolled. What is the probability of getting an even number given that the number rolled is greater than 2?
A.1/2
B.1/3
C.2/3
D.1/4
Solution
The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/4 = 1/2.
