2 Marks Questions

Question 12 Marks

Reporting time of an employee is given below :

Day	Mon	Tue	Wed	Thurs	Fri	Sat
Time (a.m.)	10:35	10:20	10:22	10:27	10:25	10:40

If the reporting time is $10: 30 a . m$., then find the probability of his coming late.

Answer

Let ' $S$ ' be the sample space and ' $E$ ' be the event that the employee is coming late.
$\therefore \quad n(S)=6$
$E=\{10: 35,10: 40\}$
$\therefore \quad n(E)=2$
$\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{2}{6}=\frac{1}{3}$
Thus, the probability of the employee coming late is $1 / 3$.

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Question 22 Marks

An experiment involves tossing of two coins and recording them in the following events
$A$ : no tail
$B$ : exactly one tail
$C$ : at least one tail.
write the sets representing events (i) $A$ and $C$ (ii) $A$ but not $B$.

Answer

When we toss two coins, the sample space is
$
\begin{array}{l}
S=\{HH, HT, TH, TT\} \\
A=\{HH\}, B=\{HT, TH\}, C=\{HT, TH, TT\}
\end{array}
$
(i) $A$ and $C=A \cap C=\phi$
(ii) $A$ but not $B=A-B=\{ HH \}$

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Question 32 Marks

In an experiment of rolling a fair $\operatorname{die}$, let $A, B$ and $C$ be three events defined as -
$A$ : a number which is a perfect square.
$B$ : a prime number.
$C$ : a number which is greater than 5 .
These events are mutually exclusive or exhaustive?

Answer

When we roll a fair die, sample space $S=\{1,2,3,4$, $5,6\}$
$
A=\{1,4\}, B=\{2,3,5\} \text { and } C=\{6\}
$
Since $A \cap B=\phi, B \cap C=\phi, C \cap A=\phi, A \cap B \cap C=\phi$.
$\therefore A, B, C$ are exhaustive events.

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Question 42 Marks

What is the probability that a given two-digit number is divisible by 15 ?

Answer

No. of two digits numbers $=90$
$\Rightarrow\quad n(S)=90$
Let ' $A$ ' be the event of getting a number divisible by 15.
$\Rightarrow \quad A=\{15,30,45,60,75,90\}$
$\Rightarrow \quad n(A)=6$
$\therefore \quad p(A)=\frac{n(A)}{n(S)}=\frac{6}{90}=\frac{1}{15}$
$\therefore$ The probability of getting a number divisible by $15=\frac{1}{15}$

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Question 52 Marks

One number is chosen at random from the number 1 to 21 . What is the probability that it is prime.

Answer

Sample space $n(S)=21$
Prime numbers from 1 to 21 are $2,3,5,7,11,13,17$, 19.
If ' $E$ ' be the event of getting a prime number, then $n(E)=8$
$\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{8}{21}$
$\therefore$ The probability that the number is prime $=\frac{8}{21}$.

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Question 62 Marks

A coin is tossed $n$ times. Find the number of elements in the sample space.

Answer

A coin has two sides, head $(H)$ and tail ( $T$ ). So, the number of elements in the sample space is $2^n$.

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Question 72 Marks

A coin is tossed. If it shows head, we draw a ball from a bag consisting of 2 red and 3 black balls. If it shows tail, coin is tossed again. Write the sample space.

Answer

Let, $R_1, R_2$ are the red balls and $B_1, B_2, B_3$ are the black balls in the bag.
$\therefore$ The sample space associated with the experiment is$
S=\left\{HR_1, HR_2, HB_1, HB_2, HB_3, TH, TT\right\}
$

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Question 82 Marks

A coin is tossed repeated until a tail comes up. Write the sample space.

Answer

Here, the sample space is
$
S=\{T, HT, HHT, H H HT, H H HHT, \ldots . . . . . . . .\}
$

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Applied Maths 2 Marks Questions

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