If $P(A|B) = P(A)$ and $P(B|A) = P(B),$ then what type of events are $A$ and $B ?$
- ✓Independent events
- BComplementary events
- CCertain events
- DImpossible events
Answer: A.
View full solution →Question types
PROBABILITY question types
307 questions across 5 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
307
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5
Question groups
5
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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 $A ∪ A’ = U,$ then what type of events are $A$ and $A’ ?$
- AIndependent variables
- ✓Complementary events
- CCertain events
- DImpossible events
Answer: B.
View full solution →Which random experiment from the following random experiment has an infinite sample space ?
- AThrowing two dice
- BSelecting two employees from an office.
- ✓To measure the life of electric bulb
- DSelect a card from $52$ cards
Answer: C.
View full solution →Which of the following statement for probability of elementary events $H$ and $T$ of a random experiment of tossing a balanced coin is not true ?
- A$P(T) = 0.5$
- B$P(H) + P(T) = 1$
- ✓$P(H T) = 0.5$
- D$P(H) = 0.5$
Answer: C.
View full solution →What is the other name of the classical definition of probability ?
- ✓Mathematical definition
- BAxiomatic definition
- CStatistical definition
- DGeometric definition
Answer: A.
View full solution →Two balanced coins are tossed simultaneously. Write the sample space of this random experiment.
State the limitations of statistical definition of probability.
State the assumptions of mathematical definition of probability.
State the characteristics of random experiment.
Give the illustrations of impossible and certain event.
The events $A_{1}$ and $A_{2}$ of a random experiment are defined as follows. Find the sets showing union event $A_{1} \cup A_{2}$ and intersection event $A_{1} \cap A_{2}$.
View full solution →Write the sample space of a random experiment of randomly selecting any one number from the natural numbers.
Write the sample space of random experiment of randomly selecting three numbers from the first four natural numbers.
Write the sample space of the random experiment of finding the number of defective items while testing the quality of $\mathbf{1 0 0 0}$ items produced in a factory.
View full solution →Two events $A$ and $B$ in the sample space of a random experiment are mutually exclusive. If $3 P(A)=4 P(B)=1$ then find $P(A \cup B)$.
View full solution →One number is randomly selected from the first $50$ natural numbers. Find the sets showing the following events.
$(1)$ The number selected is a multiple. of $5$ or $7.$
$(2)$ The number selected is a multiple of both $5$ and $7.$
$(3)$ The number selected is a multiple of 5 but not a multiple of $7.$
$(4)$ The number selected is only a multiple of $7$ out of $5$ and $7.$
View full solution →$(1)$ The number selected is a multiple. of $5$ or $7.$
$(2)$ The number selected is a multiple of both $5$ and $7.$
$(3)$ The number selected is a multiple of 5 but not a multiple of $7.$
$(4)$ The number selected is only a multiple of $7$ out of $5$ and $7.$
Two balanced dice are thrown simultaneously. Find the probability that at least one of the two dice shows the number $3 .$
View full solution →There are $3$ boys and $2$ girls in a friend-circle. Two persons are randomly selected from this friend-circle one by one with replacement to sing a song. Find the probability that the first person is a boy and the second person is a girl in the two persons selected to sing a song.
View full solution →There are $12$ screws in a box of which $4$ screws are defective. Two screws are randomly selected one by one without replacement from this box. Find the probability that both the screws selected are defective.
View full solution →If $P\left(A^{\prime}\right)=\frac{7}{25}, P(B / A)=\frac{5}{12}$ and $P(A / B)=\frac{1}{2}$ for two events $A$ and $B$ in the sample space of a random experiment then find $P(A \cap B)$ and $P(B)$.
View full solution →The events $A$ and $B$ of a random experiment are as follows $: A=\{1,2,3,4\}, B=\{-1,0,1\}$ If the sample space $U=A \cup B$ then find the sets showing the following events. $(1)\ B^{\prime}\ (2)\ A^{\prime} \cap B\ (3)\ A-B$
View full solution →There are $3$ yellow and $2$ pink flowers in a basket. One flower is randomly selected from this basket. Denote the selection of yellow flower as an event $A$ and the selection of pink flower as the event $B$. Find the sets representing the following events and answer the given questions. $ \text {(1) }U \text { (2) } A \text { (3) } B \text { (4) } A^{\prime} \text { (5) } B^{\prime} \text { (6) } A \cap B\ { (7) }\ A \cup B\ \text { (8) }\ A \cap B^{\prime}\ {(9) }\ A^{\prime} \cap B\ (10)$ State the elementary events of the sample space for this random experiment. $(11)$ Can it be said that the events $A$ and $B$ are mutually exclusive events ? Give reason. $(12)$ Can it be said that the events $A$ and $B$ are exhaustive events ? Give reason.
View full solution →A factory runs in two shifts. The sample data about the quality of items produced in these shifts are shown in the following table :
One item is randomly selected from the production of the factory.
$(1)$ If the item is taken from the production of the first shift then find the probability that it is defective.
$(2)$ If the item is defective then find the probability that it is taken from the production of the first shift.
View full solution →One item is randomly selected from the production of the factory.
$(1)$ If the item is taken from the production of the first shift then find the probability that it is defective.
$(2)$ If the item is defective then find the probability that it is taken from the production of the first shift.
The sample data obtained about marks scored by a large group of candidates appearing for a public examination of $100$ marks are given in the following table. $\begin{array}{|c|c|c|c|c|c|} \hline \text{Marks} & 20\ \text{or less} & 21-40 & 41-60 & 61-80 & 81-100 \\ \hline \text{No. of Candidates} & 83 & 162 & 496 & 326 & 124 \\ \hline \end{array}$
One candidate is randomly selected from those appearing for the public examination. Find the probability that this candidate has scored : $(1)$ less than $41$ marks $(2)$ More than $60$ marks $(3)$ Marks from $21$ to $80 .$
View full solution →One candidate is randomly selected from those appearing for the public examination. Find the probability that this candidate has scored : $(1)$ less than $41$ marks $(2)$ More than $60$ marks $(3)$ Marks from $21$ to $80 .$
Two cities $A$ and $B$ of different states have rains on $60 \%$ and $75 \%$ days respectively during the monsoon. For the cities $A$ and $B$, find the probability that on a certain monsoon day,
$(1)$ both the cities have rains
$(2)$ at least one city has rains
$(3)$ only one city has rains.
Note : The events of rains on a day in these two cities are independent.
View full solution →$(1)$ both the cities have rains
$(2)$ at least one city has rains
$(3)$ only one city has rains.
Note : The events of rains on a day in these two cities are independent.
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