Question types

Probability question types

206 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

206
Questions
5
Question groups
5
Question types
Sample Questions

Probability questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is:
  • A
    $>0.5$
  • B
    $0.5$
  • $\leq0.5$
  • D
    $0$

Answer: C.

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The probabilities of three mutually exclusive events A, B and C are given by $\frac{2}{3}$, $\frac{1}{4}$ and $\frac{1}{6}$respectively. The statement
  • A
    Is true.
  • Is false.
  • C
    Nothing can be said.
  • D
    Could be either.

Answer: B.

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If S is the sample space and $ \text{P(A)} = \frac{1}{3} \text{P(B)}$ and $\text{S} = \text{A}\cup\text{B}$ where A and B are two mutually exclusive events, then P (A) =
  • $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • C
    $\frac{3}{4}$
  • D
    $\frac{3}{8}$

Answer: A.

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A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is:
  • $\frac{64}{64}$
  • B
    $\frac{49}{64}$
  • C
    $\frac{40}{64}$
  • D
    $\frac{24}{64}$

Answer: A.

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Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is:
  • A
    $\frac{1}{5}$
  • B
    $\frac{4}{5}$
  • C
    $\frac{1}{30}$
  • $\frac{5}{9}$

Answer: D.

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Which of the following cannot be valid assignment of probability for elements or outcomes of sample space $s = W_1, W_2,W_{3,} W_4, W_5, W_6, W_7.$
Elementary events: $W_1$ $W_2$ $W_3$ $W_4$ $W_5$ $W_6$ $W_7$
  $0.7$ $0.6$ $0.5$ $0.4$ $0.3$ $0.2$ $0.1$
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Which of the following cannot be valid assignment of probability for elements or outcomes of sample space $s = W_1, W_2,W_{3,} W_4, W_5, W_6, W_7.$
Elementary events: $W_1$ $W_2$ $W_3$ $W_4$ $W_5$ $W_6$ $W_7$
  $\frac{1}{14}$ $\frac{2}{14}$ $\frac{3}{14}$ $\frac{4}{14}$ $\frac{5}{14}$ $\frac{6}{14}$ $\frac{15}{14}$
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There are three events A, B, C one of which must and only one can happen, the odds are 8 to 3 against A, 5 to 2 against B, find the odds against C.
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A bag contains $8$ red, $3$ white and $9$ blue balls. if three balls are drawn at random, determine the probability that:
  1. All the three balls are blue balls
  2. All the balls are of different colours.
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Q 163 Marks Question3 Marks
A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red?
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Q 173 Marks Question3 Marks
The probability that a person will travel by plane is $\frac{3}{5}$ and that he will travel by trains is $\frac{1}{4}.$ What is the probability that he (she) will travel by plane or train?
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Q 183 Marks Question3 Marks
In a race, the odds in favour of horses A, B, C, D are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find probability that one of them wins the race.
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An urn contains $7$ white, $5$ black and $3$ red balls. Two balls are drawn at random. Find the probability that
  1. Both the balls are red.
  2. One ball is red and the other is black.
  3. One ball is white.
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In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?
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The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English Examination is 0.75. What is the probability of passing the Hindi Examination?
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