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Statistics 1 Marks Each

PROBABILITY · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 120 questions.

Questions · Page 3 of 3

1 Marks Each

Question 1011 Mark
If $U = \{w: 0 \leq 5\ kg\};$ where w shows weight of an infant, then this is which type of sample space is called?
Answer
$U = \{w : O < w \leq 5\}$
$U = \{1, 1.1, ……. 2, 2.1, ..... 4, 4.1, 4.2; …………… 4.9, 5\}$
Here, $w =$ weight of $1$ to $5$ assumed value.
Hence $U$ is an infant sample space.
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Question 1021 Mark
“Event $A$ and complementary events $A’$ are mutually exclusive and exhaustive events.” Examine the validity of this statement.
Answer
“Event $A$ and Complementary event $A'$ are mutually exclusive and exhaustive events."
This statement is valid, because $ A \cap  A' = \emptyset$ and $A \cup A' = U$
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Question 1031 Mark
What is the value of $P(A)$ if event $A=\emptyset$ and $A=U?$
Answer
if $A = \emptyset$ then $P (A) = 0$ and $A = U$
$\therefore P (A) = 1$
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Question 1041 Mark
Are impossible and certain events are mutually exclusive and exhaustive event? Give reason for your answer.
Answer
Impossible event and certain event $‘U’$ are mutually exclusive and exhaustive events because
$\emptyset \cap\cup = \emptyset$ and $\emptyset \cap U = U.$
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Question 1051 Mark
Write the probability of impossible event and certain event.
Answer
The probability of impossible event is $‘0’ ($zero$)$ and the probability of certain event is $1.$
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Question 1061 Mark
Write the sample space for drawing two cards out of four ace randomly.
Answer
We denote four ace as $\mathrm{S}_{\mathrm{A}} ; \mathrm{C}_{\mathrm{A}} ; \mathrm{H}_{\mathrm{A}}$ and $\mathrm{D}_{\mathrm{A}}$.
Sample space of a random experiment of drawing two cards:
$U=\left\{\left(S_A, C_A\right),\left(S_A, H_A\right),\left(S_A, D_A\right),\left(C_A, H_A\right),\left(C_A, D_A\right),\left(H_A, D_A\right)\right\}$
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Question 1071 Mark
Write a elements of a sample space having three children in a family.
Answer
We take $B =$ Boy and $G =$ Girl.
The sample space for a family with three children is
$U = \{BBB, BBG, BGB, BGG, GGG, GGB, GBG, GBB\}$
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Question 1081 Mark
Write sample space of marks obtained in a $100$ marks exam.
Answer
In a $100$ marks exam minimum $‘0’ ($zero$)$ and maximum $100$ marks may be obtained.
Hence, its sample space $U = \{0, 1, 2, 3, 4, ...., 98, 99, 100\}$
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Question 1091 Mark
How many primary outcomes occur when throwing three balanced dice together?
Answer
Total primary outcomes of throwing three balanced dice together $n=6^3=216$.
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Question 1111 Mark
What is an infinite sample space?
Answer
A sample space with infinite number of elements means a sample space which is not finite is called an infinite sample space.
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Question 1121 Mark
Define sample space.
Answer
A set of all possible outcomes of a random experiment is called a sample space for that random experiment. It is denoted by the symbol $‘U’$ or $‘S’.$
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Question 1131 Mark
“Adding ten to ten is twenty”. Is this event a random event? Give reason for your answer.
Answer
“Adding ten to ten is twenty.” This event is not a random event because it does not depend on chance.
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Question 1151 Mark
Which word is used for the chance that a random event occurs?
Answer
The word probability is used for the chance that a random event occurs.
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Question 1171 Mark
Write definition of elementary events.
Answer
Events consisting of only a single element of a sample space $U$ are called elementary events. Elementary events are mutually exclusive and exhaustive events.
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Question 1181 Mark
Define mutually exclusive events.
Answer
Two events A and B are said to be mutually exclusive if they cannot occur simultaneously, i.e., $A \cap B = \emptyset$.
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Question 1191 Mark
Arrange $P(A\cup B), P(A), P(A\cap B), 0, P(A)+P(B)$ in the ascending order.
Answer
The ascending order is :
0 $\le P(A\cap B) \le P(A) \le P(A\cup B) \le P(A)+P(B)$
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Question 1201 Mark
Arrange $P(A \cup B)$, 1, $P(A)$, $P(A \cap B)$, 0, $P(A)+P(B)$ in the ascending order.
Answer
$0 < P(A \cap B) < P(A) < P(A \cup B) < 1 < P(A)+P(B)$
Note : This assumes A and B are overlapping events within the same space.
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