Mathematics

Probability

337 Questions

Probability measures the likelihood of an event occurring, such as rolling a specific number on a die or drawing a colored ball. Questions cover simple events, mutually exclusive outcomes, and dice or coin combinations. This topic is consistently asked in mathematics and reasoning sections of competitive exams.

dice probabilitycoin toss eventsdrawing balls probabilitiesplaying card problemsmutually exclusive events

Probability Questions

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 5 green balls. If a ball is randomly drawn from the bag, what is the probability that it is not green?

  1. (25/30)

  2. (5/30)

  3. (10/30)

  4. (15/30)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total number of balls in the bag is 10 + 15 + 5 = 30. The number of balls that are not green is 10 + 15 = 25. So, the probability of drawing a ball that is not green is 25/30.

Multiple choice

A coin is tossed twice. What is the probability of getting two heads?

  1. (1/4)

  2. (1/2)

  3. (3/4)

  4. (1/8)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are four possible outcomes when a coin is tossed twice: HH, HT, TH, TT. Only one of these outcomes, HH, results in two heads. So, the probability of getting two heads is 1/4.

Multiple choice

A box contains 6 red balls, 4 blue balls, and 2 green balls. If two balls are randomly drawn from the box without replacement, what is the probability that both balls are red?

  1. (3/10)

  2. (1/5)

  3. (2/5)

  4. (1/2)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of drawing a red ball on the first draw is 6/12 = 1/2. After the first draw, there are 5 red balls and 11 total balls remaining in the box. So, the probability of drawing a red ball on the second draw is 5/11. The probability of both events occurring is (1/2) * (5/11) = 1/5.

Multiple choice

A bag contains 10 white balls, 15 black balls, and 5 red balls. If 4 balls are randomly drawn from the bag without replacement, what is the probability that exactly 2 of the balls are white?

  1. (3/14)

  2. (1/7)

  3. (2/7)

  4. (4/7)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing a white ball on the first draw is 10/30. After the first draw, there are 9 white balls and 29 total balls remaining in the bag. So, the probability of drawing a white ball on the second draw is 9/29. After the second draw, there are 8 white balls and 28 total balls remaining in the bag. So, the probability of drawing a white ball on the third draw is 8/28. After the third draw, there are 7 white balls and 27 total balls remaining in the bag. So, the probability of drawing a white ball on the fourth draw is 7/27. The probability of exactly 2 of the balls being white is (10/30) * (9/29) * (8/28) * (19/27) = 2/7.

Multiple choice

A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?

  1. (1/6)

  2. (1/3)

  3. (1/2)

  4. (5/12)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There are 36 possible outcomes when a fair six-sided die is rolled twice. The outcomes that result in a sum of 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 5 green balls. If 3 balls are randomly drawn from the bag without replacement, what is the probability that all 3 balls are of different colors?

  1. (1/14)

  2. (2/7)

  3. (3/14)

  4. (4/7)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing a red ball on the first draw is 10/30. After the first draw, there are 9 red balls, 15 blue balls, and 4 green balls remaining in the bag. So, the probability of drawing a blue ball on the second draw is 15/29. After the second draw, there are 9 red balls, 14 blue balls, and 4 green balls remaining in the bag. So, the probability of drawing a green ball on the third draw is 4/28. The probability of all three events occurring is (10/30) * (15/29) * (4/28) = 3/14.

Multiple choice

A fair coin is tossed 10 times. What is the probability of getting exactly 5 heads?

  1. (1/1024)

  2. (1/512)

  3. (1/256)

  4. (1/128)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting a head on a single toss is 1/2. The probability of getting a tail on a single toss is also 1/2. The probability of getting exactly 5 heads in 10 tosses is given by the binomial distribution: P(X = 5) = (10 choose 5) * (1/2)^5 * (1/2)^5 = 252 * 1/32 = 1/256.

Multiple choice

A box contains 12 red balls, 18 blue balls, and 6 green balls. If 4 balls are randomly drawn from the box without replacement, what is the probability that there are exactly 2 red balls and 2 blue balls?

  1. (1/14)

  2. (1/7)

  3. (2/7)

  4. (3/14)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing a red ball on the first draw is 12/36. After the first draw, there are 11 red balls, 18 blue balls, and 6 green balls remaining in the box. So, the probability of drawing a red ball on the second draw is 11/35. After the second draw, there are 10 red balls, 18 blue balls, and 6 green balls remaining in the box. So, the probability of drawing a blue ball on the third draw is 18/34. After the third draw, there are 10 red balls, 17 blue balls, and 6 green balls remaining in the box. So, the probability of drawing a blue ball on the fourth draw is 17/33. The probability of all four events occurring is (12/36) * (11/35) * (18/34) * (17/33) = 2/7.

Multiple choice

A bag contains 15 red balls, 10 blue balls, and 5 green balls. If 4 balls are randomly drawn from the bag without replacement, what is the probability that there are more red balls than blue balls?

  1. (1/2)

  2. (2/5)

  3. (3/5)

  4. (4/5)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

There are 5 possible outcomes where there are more red balls than blue balls: (3 red, 1 blue), (3 red, 1 green), (2 red, 2 blue), (2 red, 1 green, 1 blue), and (1 red, 3 blue). The probability of each of these outcomes is given by the multinomial distribution: P(X = 3 red, 1 blue) = (4 choose 3) * (15 choose 3) * (10 choose 1) / (30 choose 4) = 1350 / 27405, P(X = 3 red, 1 green) = (4 choose 3) * (15 choose 3) * (5 choose 1) / (30 choose 4) = 675 / 27405, P(X = 2 red, 2 blue) = (4 choose 2) * (15 choose 2) * (10 choose 2) / (30 choose 4) = 2700 / 27405, P(X = 2 red, 1 green, 1 blue) = (4 choose 2) * (15 choose 2) * (5 choose 1) * (10 choose 1) / (30 choose 4) = 1350 / 27405, and P(X = 1 red, 3 blue) = (4 choose 1) * (15 choose 1) * (10 choose 3) / (30 choose 4) = 675 / 27405. The probability of more red balls than blue balls is the sum of these probabilities: 1350/27405 + 675/27405 + 2700/27405 + 1350/27405 + 675/27405 = 6750/27405 = 3/5.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that the ball is blue?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcomes are the number of blue balls, which is 15. The total number of possible outcomes is the total number of balls, which is $10 + 15 + 20 = 45$. Therefore, the probability of selecting a blue ball is $rac{15}{45} = rac{1}{3}$.

Multiple choice

A bag contains 12 red balls, 18 blue balls, and 24 green balls. If a ball is randomly selected from the bag, what is the probability that the ball is green?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcomes are the number of green balls, which is 24. The total number of possible outcomes is the total number of balls, which is $12 + 18 + 24 = 54$. Therefore, the probability of selecting a green ball is $rac{24}{54} = rac{1}{2}$.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that it is a green ball?

  1. \(\frac{1}{2}\)
  2. \(\frac{1}{3}\)
  3. \(\frac{2}{5}\)
  4. \(\frac{1}{5}\)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the probability of selecting a green ball, we need to divide the number of green balls (20) by the total number of balls (10 + 15 + 20 = 45). Therefore, the probability is (\frac{20}{45} = \frac{2}{5}).

Multiple choice

What is the probability of getting a head when flipping a coin?

  1. \(\frac{1}{2}\)
  2. \(\frac{1}{3}\)
  3. \(\frac{1}{4}\)
  4. \(\frac{1}{6}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When flipping a coin, there are two possible outcomes: head or tail. Since both outcomes are equally likely, the probability of getting a head is (\frac{1}{2}).

Multiple choice

What is the mathematical principle that is used to determine the outcome of a dice roll in Indian gambling games?

  1. Probability

  2. Statistics

  3. Calculus

  4. Algebra
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability is the mathematical principle that is used to determine the outcome of a dice roll in Indian gambling games. It involves the calculation of the likelihood of different outcomes.

Multiple choice

What is the probability of getting a head when flipping a coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When flipping a coin, there are two possible outcomes: head or tail. Therefore, the probability of getting a head is 1/2.