Exercise 32.1
Page no 32.10
Type 1
Question 1
In each of the following exercises (i) to (iv), describe the sample space for the given experiments.
(i) a coin is tossed two times.
(ii) a coin is tossed three times.
(iii) a coin is tossed and then a die is rolled if a head shows on the coin.
(iv) a coin and a die are tossed simultaneously.
(v) a coin is tossed four times.
(vi) a die is thrown two times.
Question 2
Two well-balanced dice are rolled and the numbers that turn up are observed. Determine the sample space.
Question 3
(i) A box contains 1 blue and 3 white balls. Two balls are drawn in succession without replacement from the box. What is the sample space for this experiment.
(ii) One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its upper most face is noted. Describe the sample space.
Question 4
A coin is tossed. If it shows a head, a diE is thrown and if the die shows up an odd number, the die is thrown again. Describe the sample space for this experiment.
Question 5
(i) An experiment is performed in which a die is rolled and then a coin is tossed if the number on the die is even. If the number on the die is odd. the coin is tossed twice. Describe the sample space for this experiment.
(ii) An experiment consists of recording boy-girl composition of families with 2 children.
(a) What is the sample space if we are interested in knowing whether it is a boy or a girl in the order of their births?
(b) What is the sample space if we are interested in the number of girls in the family ?
Question 6
There are 2 boys and 2 girls in group $A$ and 1 boy and 3 girls in group $B$. Write the sample space for the experiment in which a group is selected and then a person from that group.
Question 7
A box contains 3 identical red balls and 3 identical blue balls. An experiment consists of drawing one ball with replacement and again drawing a ball. What are the possible outcomes of the experiment?
Question 8
A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.
Question 9
In a random experiment, three articles are selected from a lot. Each article is tested and classified as defective $(D)$ or perfect $(P)$. Write the sample space of this experiment.
Page no 32.11
Question 10
Three coloured dice of red, white and blue colours are placed in a bag. One die is drawn at random from the bag and its colour and the number appearing on its top face is noted. Describe the sample space for this experiment.
Question 11
(i) A coin is tossed repeatedly until a head appears for the first time. Describe the sample space for the experiment.
(ii) A die is thrown repeatedly until a six comes up. What is the sample space for this experiment.
Question 12
A coin is tossed two times. Writes all its events.
Question 13
A die is rolled . Let A denote the event "die shown 3" and B denote the event the die shows an odd number " . Are A and B mutually exclusive ?
Question 14
Two dice are thrown. The sum of the numbers appearing on the top face of both the dice are noted. Describe the events :
(i) A: sum is less than 7
(ii) $B:$ sum is greater than 13
(iii) $C$ : sum is an even number
(iv) $D$ : sum is greater than 11
(v) $E$ : sum is a multiple of 5
Question 15
For the question (14) find
(i) $A \cup B$
(ii) $A \cap B$
(iii) $D \cap B^{\prime}$
(iv) $D \cup(A \cap C)$
Question 16
A die is thrown twice, the numbers appearing on the top face are recorded. Describe the events :
$A$ : both the numbers are odd.
$B$ : both the numbers are even.
Describe $A \cup B$ and $A \cap B$. Are the two events mutually exclusive ?
Question 17
Two dice are thrown. The events $A, B, C$ and $D$ are as follows :
$A$ : getting an even number on the first die
$B$ : getting an odd number on the first die
$C$ : getting a sum of 2
$D$ : getting an odd number on one of the dice
State whether the following statements are true or false.
(i) $A$ is a simple event.
(ii) $C$ is a simple event.
(iii) $A$ and $B$ are mutually exclusive. (iv) $A^{\prime}$ and $B^{\prime}$ are mutually exclusive.
(v) $A=B^{\prime}$
(vi) $A$ and $B$ are mutually exhaustive
(vii) $A, B$ and $D$ are mutually exclusive and exhaustive events.
Question 18
A coin is tossed once. A die is rolled if head turns up and the coin is tossed twice if a tail appears. Describe the events
(i) "Exactly one head occurs"
(ii) "at least two tails occur"
(iii) "s number greater than 4 occurs"
Page no 32.13
Question 19
In the experiment of "tossing a coin thrice" consider the events
$A$ : 'Exactly one head appeared"
$B$ : 'At least one head appeared'
C: "Atmost one head appeared" etc.
Examine which of them are compound events ?
Question 20
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events :
$A$ : the sum is greater than 8
$B: 2$ occurs on either die
$C$ : the sum is at least 7 and a multiple of 3 .
Which pair of these events are mutually exclusive?
Question 21
Two dice are thrown. The events $A, B$ and $C$ are as follows :
$A$ : getting an even number on the first die
$B$ : getting an odd number on the first die
$C$ : getting the sum of the numbers on the dice $\leq 5$
Describe the following events :
(i) $A^{*}$
(ii) not $B$
(iii) $A$ or $B$
(iv) $A$ and $B$
(v) $A$ but not $C$
(vi) $B$ or $C$
(vii) $B$ and $C$
(viii) $A \cap B^{*} \cap C^{\circ}$
Question 22
Three coins are tossed once. Let $A$ denote the event "three heads show", $B$ denote the event "two heads and one tail show", $C$ denote the event three tails show and $D$ denote the event "a head shows on the first coin". Which events are :
(i) mutually exclusive ?
(ii) simple ?
(iii) compound?
Question 23
Three coins are tossed. Describe
(i) Two events which are mutually exclusive.
(ii) Three events which are mutually exclusive and exhaustive.
(iii) Two events, which are not mutually exclusive.
(iv) Two events which are mutually exclusive but not exhaustive.
(v) Three events which are mutually exclusive but not exhaustive.
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