Mathematics

Probability

303 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

One ticket is drawn at random from a bag containing 30 tickets numbered from 1 to 30. What is the probability that it is a multiple of 3 or 5?

  1. 7/15

  2. 2/5

  3. 1/2

  4. 1/5

  5. -
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total numbers upto 30 divisible by 3 = 10 Total numbers divisible by 5 = 6 Numbers divisible by 3 and 5 = 2 Total numbers divisible by 3 and 5 = 10 + 6 - 2 = 14 So, the probability of getting a number divisible by 3 or 5 = 14/30 = 7/15 Option 1 is correct.

Multiple choice

The odds in favour of winning a game of chess, against b, are 5/2. If three games are to be played, the odds in favour of a's winning, at least in one game, are

  1. 335/8

  2. 1/2

  3. 8/335

  4. None of these

  5. -
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Odds in favour of ‘a’ winning = 5/2 Probability of ‘a’ to win match = 5/7 Probability that ‘a’ wins at least one match out of three = 1 – (2/7 x2/7 x 2/7) = 335/343 Odds in favour of winning at least one match = 335/8 Option 1 is correct.

Multiple choice

There are two containers, with one containing 4 red and 3 green balls and the other containing 3 blue and 4 green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be

  1. 1/7

  2. 9/49

  3. 12/49

  4. 3/7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing a red ball from the first container is 4/7. The probability of drawing a blue ball from the second container is 3/7. Since these are independent events, the probability of both occurring is (4/7) * (3/7) = 12/49.

Multiple choice

Directions: Carry Two Marks Each.

A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in the three tosses. Based on the above information, which of the following statements is TRUE?

  1. X and Y are not independent.

  2. Y and Z are dependent.

  3. Y and Z are independent.

  4. X and Z are independent.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a coin tossed 3 times, Let X be the event that head occurs in each of the first two tosses. So, set X = {HHT, HHH} Now, let Y be the event that a tails occurs on the third toss. Statement implies first two must be heads for tails in third toss. Set Y = {HHT} It implies event Y is dependent on event X. Now, let Z be the event that two tails occur in the three tosses. So, set Z = {TTH, TTT, THT, HTT} Now, we can see that event X and event Z are independent as their sets have no common occurrence.