Question types

PART 2 : PROBABILITY question types

88 questions across 4 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.

88
Questions
4
Question groups
5
Question types
Sample Questions

PART 2 : PROBABILITY questions

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

Q 1MCQ1 Mark
What is the value of $P\left(A^{\prime} \cup A\right)$ for complementary events $A$ and $A^{\prime} ?$
  • $1$
  • B
    $0$
  • C
    $0.5$
  • D
    Between $0$ and $1$

Answer: A.

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Q 2MCQ1 Mark
Which of the following options is true for $P(A \cup B)$ for two exhaustive events $A$ and $B$ ?
  • A
    $P(A \cup B)=P(A)+P(B)$
  • $P(A \cup B)=P(U)$
  • C
    $P(A \cup B)=P\cdot P(B)$
  • D
    $P(A \cup B)=P(A)-P(B)$

Answer: B.

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Q 3MCQ1 Mark
Which of the following options is true for mutually exclusive events $A$ and $B$ that are not exhaustive?
  • A
    $P(B / A)=P(B)$
  • B
    $P(A / B)=P(A)$
  • C
    $P(A \cup B)=1$
  • $P(A-B)=P(A)$

Answer: D.

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Q 4MCQ1 Mark
From the following random experiments, which random experiment has infinite sample space?
  • A
    Selecting a card at random from $52$ cards
  • B
    Selecting $5$ schools at random from the schools of a city
  • C
    Selecting an item at random from a lot of items
  • Measuring weight of an infant

Answer: D.

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Q 5MCQ1 Mark
What will be $(A \cap B) \cup\left(A \cap B^{\prime}\right)$ from the following ?
  • A
    $A^{\prime}$
  • B
    $B$
  • $A$
  • D
    $A^{\prime} \cap B^{\prime}$

Answer: C.

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Q 61 Marks Each1 Mark
According to the mathematical definition of probability, what is the probability of each outcome out of $n$ outcomes of a random experiment?
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Q 112 Marks Each2 Marks
Two cards are selected from a pack of $52$ cards one by one without replacement. Find the probability of getting an ace and a king in that order.
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Q 132 Marks Each2 Marks
There are $3$ yellow and $7$ white flowers in a basket. Two flowers are selected one by one without replacement from it. Find the probability that the first flower is yellow and the second flower is white.
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Q 142 Marks Each2 Marks
$7$ eitizens of country $A$ and $5$ citizens of country $B$ are traveling in an international flight of a company. After the routine security check, a higher level officer randomly selects $2$ citizens without replacement from the citizens of these two countries for additional security. Find the probability that both the selected citizens are from different countries.
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Q 163 Marks Each3 Marks
A factory is woking in two shifts. The following table shows the sample information regarding the quality of goods produced in these shifts,
Quality Shift
$1$ $11$
Defective Units $20$ $40$
Non-defective Units $100$ $150$
One unit is selected at random from the factory.
$(1)$ If the unit is selected from the first shift, find the probability that it is defective.
$(2)$ If the unit is defective, find the probability that it is from the production of second shift.
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Q 173 Marks Each3 Marks
There are two lifts $($Elevators$) E _1$ and $E _2$ in a multistorey building.
The probability that each one is in working condition is $0.9$. Find probability that,
at any point of time,
$(1)$ Only one of the lifts is in working condition.
$(2)$ Both the lifts are in working condition.
$(3)$ None of the lifts is in working condition.
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Q 183 Marks Each3 Marks
A person has two aquariums at his home. There are $5$ Catfishes and $3$ Guppy fishes in first aquarium and $4$ Catfishes and $4$ Guppy fishes in the second aquarium. The person selects one aquarium at random and then selects one fish from it to gift it to his friend keeping the aquarium at his home. Find probability that the gifted fish is Guppy. $($Catfish and Guppy are names of species of fishes.$)$
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Q 193 Marks Each3 Marks
There are $3$ students from Ahmedabad and $2$ students from Surat securing ranks in top ten in the $CA$ result declared in a certain year. Whereas, in $CS$ result, such students are $2$ and $4$ respectively. A multinational company selects one $CA$ and one $CS$ from these students for the job. Find the probability that both the selected students are from the same city.
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Q 203 Marks Each3 Marks
$11$ employees working in a company are busy wsing their smart phones during recess period.
Of them, $6$ employees are busy using application $W$ and the rest are busy using application
$F$. Two employees are selected at random from these employees with replacement. Find
probability that,
$(1)$ Both the employees are busy using application $W.$
$(2)$ One of those two employees is busy using application $F$.
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