Question 13 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. Answer$(1)\ \frac{1}{6}$
$(2)\ \frac{2}{3}$
View full question & answer→Question 23 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.
Answer$(1)\ 0.18\ (2)\ 0.81\ (3)\ 0.01$
View full question & answer→Question 33 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.$)$
View full question & answer→Question 43 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.
View full question & answer→Question 53 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 $F$.
Answer$\frac{36}{121}, \frac{60}{121}$
View full question & answer→Question 63 Marks
If $P(A)=0.6, P(B)=0.7$ and $P(A \cap B)=0.4$, find $P\left(A^{\prime} / B^{\prime}\right)$ and $P\left(B^{\prime} / A^{\prime}\right)$.
Answer$\frac{3}{7}, \frac{1}{4}$
View full question & answer→Question 73 Marks
If $P(A)=\frac{1}{3}, P(B)=\frac{2}{3}$ and $P(A / B)=\frac{1}{4}$, find $P\left(A^{\prime} \cap B^{\prime}\right)$.
View full question & answer→Question 83 Marks
If $P(B-A)=0.3, P(A)=0.7$ and $P\left(B^{\prime}\right)=0.4$, find $P(A / B)$ and $P(B / A)$.
Answer$\frac{1}{2}, \frac{3}{7}$
View full question & answer→Question 93 Marks
If $1.5 P(A)=2 P(B)=P(A \cup B)=0.9$, find $P(A / B)$ and $P(B / A)$.
Answer$\frac{1}{3}, \frac{1}{4}$
View full question & answer→Question 103 Marks
One number is selected at random from the first $30$ natural numbers. If the selected number is a multiple $2 ,$ find the probsbility that the number is also a multiple of $5.$
View full question & answer→Question 113 Marks
Two balanced dice are thrown simultaneously. If it is known that the sum of digits on two dice is greater than $6 ,$ find probability that both the digits on two dice are different.
View full question & answer→Question 123 Marks
An unbinsed coin is tossed three times, If it is head when the coin is tossed the first time, find the probability that all three times head is obtained.
Question 133 Marks
For two events $A$ and $B$ of the sample space of a random experiment, $P\left(A^{\prime}\right)=0.2, P(B)=0.7$ and $P(A \cup B)=0.93$. Find $P\left(A \cap B^{\prime}\right)$ and $P\left(A^{\prime} \cap B\right)$.
View full question & answer→Question 143 Marks
Three events $A , B$ and $C$ of a sample space are mutually exclusive and exhaustive. If $2 P(A)=3 P(B)=4 P(C)$ then find $P(A \cup B)$ and $P(B \cup C)$
Answer$(1)\ \frac{10}{13}$
$(2)\ \frac{7}{13}$
View full question & answer→Question 153 Marks
For two events $A$ and $B$ of the sample space of a random experiment, $2 P(A)=3 P(B)=4 P(A \cap B)=0.6$. Obtain the probabilities for the following events.
$(1)\ \left(A^{\prime} \cap B^{\prime}\right)$
$(2)\ (A-B)$
$(3)\ \left(A^{\prime} \cap B\right)$
Answer$(1)\ 0.65\ (2)\ 0.15\ (3)\ 0.05$
View full question & answer→Question 163 Marks
On a holiday, the probabilities that a student studying in the $12th$ Standard revises
Statistics subject, Economics subject and both the subjects are $0.72,0.66$ and $0.48$
respectively. One student of the $12 th$ standard is selected at random. Find the probability, that on a holiday, he revises
$(1)$ At least one subject out of Statistics and Economics.
$(2)$ None of the subject out of Statistics and Economics.
$(3)$ Any one subject out of Statistics and Economics.
Answer$(1)\ 0.9\ (2)\ 0.1\ (3)\ 0.42$
View full question & answer→Question 173 Marks
From first $20$ natural numbers, one number is selected at random. Find the probability that the number is even or divisible by $5 .$
View full question & answer→Question 183 Marks
Among $40$ students studying in a class, $30$ are boys and $10$ are girls, $18$ boys and $4$ girls got $A ^{+}$grade in an examination. A student is selected from this class. Find probability that the student is a boy or a student having $A ^{+}$grade.
View full question & answer→Question 193 Marks
One card is selected at random from a pack of $52$ cards
Find the probability that the selected card is
$(1)$ A spade or a jack.
$(2)$ Neither a spade nor a jack.
Answer$(1) \frac{4}{13}$
$(2) \frac{9}{13}$
View full question & answer→Question 203 Marks
Find the probability that a randomly selected number from the first $100$ natural numbers is a multiple of $3$ or $4 .$
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